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#linearalgebra — Public Fediverse posts

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  1. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Dot Product:** A scalar value measuring how much two vectors point in the same direction.
    Ex: For `u=[1,2], v=[3,4] -> u.v = (1*3)+(2*4)=11`.
    Pro-Tip: If `u.v = 0`, the vectors are orthogonal (perpendicular)!
    #LinearAlgebra #VectorMath #STEM #StudyNotes

    #linearalgebra #vectormath #stem #studynotes
  2. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Dot Product:** A scalar value measuring how much two vectors point in the same direction.
    Ex: For `u=[1,2], v=[3,4] -> u.v = (1*3)+(2*4)=11`.
    Pro-Tip: If `u.v = 0`, the vectors are orthogonal (perpendicular)!
    #LinearAlgebra #VectorMath #STEM #StudyNotes

    #linearalgebra #vectormath #stem #studynotes
  3. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Determinant:** A single scalar value derived from a square matrix.
    Ex: For `[[a,b],[c,d]]`, `det = ad - bc`.
    Pro-Tip: If `det = 0`, the matrix is NOT invertible (no unique solution for systems!).
    #LinearAlgebra #MatrixTips #STEM #StudyNotes

    #linearalgebra #matrixtips #stem #studynotes
  4. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Determinant:** A single scalar value derived from a square matrix.
    Ex: For `[[a,b],[c,d]]`, `det = ad - bc`.
    Pro-Tip: If `det = 0`, the matrix is NOT invertible (no unique solution for systems!).
    #LinearAlgebra #MatrixTips #STEM #StudyNotes

    #linearalgebra #matrixtips #stem #studynotes
  5. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Matrix Addition:** Combine matrices by adding their corresponding elements.
    Ex: If A=[1,2;3,4] & B=[5,6;7,8], then A+B = [6,8;10,12].
    Pro-Tip: They MUST have the same dimensions to add them!
    #LinearAlgebra #MatrixMath #STEM #StudyNotes

    #linearalgebra #matrixmath #stem #studynotes
  6. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Matrix Addition:** Combine matrices by adding their corresponding elements.
    Ex: If A=[1,2;3,4] & B=[5,6;7,8], then A+B = [6,8;10,12].
    Pro-Tip: They MUST have the same dimensions to add them!
    #LinearAlgebra #MatrixMath #STEM #StudyNotes

    #linearalgebra #matrixmath #stem #studynotes
  7. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Dot Product:** A scalar indicating how much two vectors point in the same direction.
    Ex: For `v=[1,2]` & `u=[3,4]`, `v.u = (1*3) + (2*4) = 11`.
    Pro-Tip: If `v.u = 0`, the vectors are orthogonal (perpendicular)!
    #LinearAlgebra #VectorMath #STEM #StudyNotes

    #linearalgebra #vectormath #stem #studynotes
  8. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Dot Product:** A scalar indicating how much two vectors point in the same direction.
    Ex: For `v=[1,2]` & `u=[3,4]`, `v.u = (1*3) + (2*4) = 11`.
    Pro-Tip: If `v.u = 0`, the vectors are orthogonal (perpendicular)!
    #LinearAlgebra #VectorMath #STEM #StudyNotes

    #linearalgebra #vectormath #stem #studynotes
  9. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Linear Combination:** Sum of vectors multiplied by scalars.
    Ex: `c1*v1 + c2*v2`
    Pro-Tip: Fundamental for understanding span & basis for vector spaces!
    #LinearAlgebra #VectorMath #STEM #StudyNotes

    #linearalgebra #vectormath #stem #studynotes
  10. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Linear Combination:** Sum of vectors multiplied by scalars.
    Ex: `c1*v1 + c2*v2`
    Pro-Tip: Fundamental for understanding span & basis for vector spaces!
    #LinearAlgebra #VectorMath #STEM #StudyNotes

    #linearalgebra #vectormath #stem #studynotes
  11. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Dot Product:** A scalar result measuring how much two vectors point in the same direction.
    Ex: For `v=[a,b], w=[c,d]`, `v.w = ac+bd`.
    Pro-Tip: If `v.w = 0`, vectors are orthogonal (perpendicular)!
    #LinearAlgebra #VectorMath #STEM #StudyNotes

    #linearalgebra #vectormath #stem #studynotes
  12. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Dot Product:** A scalar result measuring how much two vectors point in the same direction.
    Ex: For `v=[a,b], w=[c,d]`, `v.w = ac+bd`.
    Pro-Tip: If `v.w = 0`, vectors are orthogonal (perpendicular)!
    #LinearAlgebra #VectorMath #STEM #StudyNotes

    #linearalgebra #vectormath #stem #studynotes
  13. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Linear Independence:** Vectors are LI if no vector can be expressed as a linear combo of the others.
    Ex: For `c1*v1 + c2*v2 = 0`, only `c1=c2=0` works.
    Pro-Tip: LI vectors are unique & don't introduce redundant info. Key for basis & unique solutions!
    #LinearAlgebra #VectorSpaces #STEM #StudyNotes

    #linearalgebra #vectorspaces #stem #studynotes
  14. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Linear Independence:** Vectors are LI if no vector can be expressed as a linear combo of the others.
    Ex: For `c1*v1 + c2*v2 = 0`, only `c1=c2=0` works.
    Pro-Tip: LI vectors are unique & don't introduce redundant info. Key for basis & unique solutions!
    #LinearAlgebra #VectorSpaces #STEM #StudyNotes

    #linearalgebra #vectorspaces #stem #studynotes
  15. kipriyanovich @[email protected] ·

    Alright, future engineers!

    **Eigenvector:** A non-zero vector whose direction doesn't change when transformed by a matrix. It only scales!
    Ex: `Av = λv`, where `v` is the eigenvector & `λ` its eigenvalue.
    Pro-Tip: They uncover the natural directions of a matrix's action. Essential for system stability!
    #LinearAlgebra #EigenStuff #STEM #StudyNotes

    #linearalgebra #eigenstuff #stem #studynotes
  16. kipriyanovich @[email protected] ·

    Alright, future engineers!

    **Eigenvector:** A non-zero vector whose direction doesn't change when transformed by a matrix. It only scales!
    Ex: `Av = λv`, where `v` is the eigenvector & `λ` its eigenvalue.
    Pro-Tip: They uncover the natural directions of a matrix's action. Essential for system stability!
    #LinearAlgebra #EigenStuff #STEM #StudyNotes

    #linearalgebra #eigenstuff #stem #studynotes
  17. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Matrix Multiplication:** Produces a new matrix by combining rows of the first with columns of the second.
    Ex: For `C = AB`, `C_ij = sum(A_ik * B_kj)`.
    Pro-Tip: Inner dimensions MUST match! `(m x n) * (n x p)` gives `(m x p)`.
    #MatrixMath #LinearAlgebra #STEM #StudyNotes

    #matrixmath #linearalgebra #stem #studynotes
  18. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Matrix Multiplication:** Produces a new matrix by combining rows of the first with columns of the second.
    Ex: For `C = AB`, `C_ij = sum(A_ik * B_kj)`.
    Pro-Tip: Inner dimensions MUST match! `(m x n) * (n x p)` gives `(m x p)`.
    #MatrixMath #LinearAlgebra #STEM #StudyNotes

    #matrixmath #linearalgebra #stem #studynotes
  19. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Dot Product:** A scalar value indicating how much two vectors point in the same direction.
    Ex: For `u=[1,2]`, `v=[3,4]`, `u.v = (1*3) + (2*4) = 11`.
    Pro-Tip: If `u.v = 0`, the vectors are orthogonal (perpendicular)! Key for geometric analysis!
    #VectorMath #LinearAlgebra #STEM #StudyNotes

    #vectormath #linearalgebra #stem #studynotes
  20. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Dot Product:** A scalar value indicating how much two vectors point in the same direction.
    Ex: For `u=[1,2]`, `v=[3,4]`, `u.v = (1*3) + (2*4) = 11`.
    Pro-Tip: If `u.v = 0`, the vectors are orthogonal (perpendicular)! Key for geometric analysis!
    #VectorMath #LinearAlgebra #STEM #StudyNotes

    #vectormath #linearalgebra #stem #studynotes
  21. Yuriy Karetin @[email protected] ·

    MVspa_ Stochastic processes
    Стохастические процессы, Випадкові процеси
    #Stochastic processes
    #Стохастическиепроцессы, #Випадковіпроцеси
    t.me/scilib_yura15cbx/230

    MVsa Statistics and applications
    Статистика та додатки, Статистика и приложения
    #Statistics
    t.me/scilib_yura15cbx/229

    EM_ Mechanics of elastic materials
    Механіка пружних матеріалів, Механика упругих материалов
    t.me/scilib_yura15cbx/228

    MPd_ Dynamical systems
    Динамические системы, Динамічні системи
    #Dynamical systems
    t.me/scilib_yura15cbx/227

    MNw_ Wavelets, signal processing
    Вейвлети, обробка сигналів, Вейвлеты, обработка сигналов
    #Wavelets, #signal processing
    t.me/scilib_yura15cbx/226

    MNs_ Simulations of physics
    Физические симуляции
    t.me/scilib_yura15cbx/225

    MNl_ Numerical linear algebra
    Числова лінійна алгебра, Численная линейная алгебра
    t.me/scilib_yura15cbx/224

    MNf_ Finite elements
    Конечные элементы, Скінченні елементи
    t.me/scilib_yura15cbx/223

    MNd_ Numerical calculus
    t.me/scilib_yura15cbx/222

    MDgt_ General topology
    #topology
    Общая топология, Загальна топологія
    t.me/scilib_yura15cbx/221

    MDdg_ Differential geometry
    Диференціальна геометрія, Дифференциальная геометрия
    t.me/scilib_yura15cbx/220

    MDat_ Algebraic and differential topology
    Алгебраическая и дифференциальная топология, Алгебраїчна та диференціальна топологія
    t.me/scilib_yura15cbx/219

    MCv_ Variational calculus
    Варіаційне числення, Вариационное исчисление
    t.me/scilib_yura15cbx/218

    MCta_ Tensor calculus, forms
    Тензорное исчисление, формы, Тензорне числення, форми
    t.me/scilib_yura15cbx/217

    MCsf_ Special functions
    Спеціальні функції, Специальные функции
    t.me/scilib_yura15cbx/216

    MCf_ Functional analysis
    Функциональный анализ, Функціональний аналіз
    t.me/scilib_yura15cbx/215

    MCet_ Elementary calculus textbooks
    Підручники з елементарного числення, Учебники по элементарному исчислению
    t.me/scilib_yura15cbx/214

    MCde_ Differential equations
    Дифференциальные уравнения, Диференціальні рівняння
    #Differential equations
    t.me/scilib_yura15cbx/213

    MCcf_ Continued fractions
    Суцільні дроби, Непрерывные дроби
    t.me/scilib_yura15cbx/212

    MCc_ Complex variable
    Комплексная переменная, Комплексна змінна
    t.me/scilib_yura15cbx/211

    MCat_ Advanced calculus
    t.me/scilib_yura15cbx/210

    Asymptotics, perturbations
    Асимптотика, збурення,
    Асимптотика, возмущения
    #Asymptotics, #perturbations
    #Асимптотика, #збурення,
    #Асимптотика, #возмущения
    t.me/scilib_yura15cbx/209

    Group theory, Теория групп, Теорія груп
    #Group theory, #Теориягрупп, #Теоріягруп
    t.me/scilib_yura15cbx/208

    Algebra textbooks,
    Підручники з алгебри,
    Учебники по алгебре
    t.me/scilib_yura15cbx/207

    Set theory,
    Теория множеств, Теорія множин
    #Set theory,
    #Теория множеств,
    t.me/scilib_yura15cbx/206

    Representation theory
    Теорія репрезентації, Теория представлений
    t.me/scilib_yura15cbx/205

    Quantum groups
    #Quantum groups
    Квантовые группы, Квантові групи
    t.me/scilib_yura15cbx/204

    Mathematical logic
    #Mathematical logic
    Математична логіка, Математическая логика
    t.me/scilib_yura15cbx/203

    Linear algebra
    #Linear algebra
    Линейная алгебра, Лінійна алгебра
    t.me/scilib_yura15cbx/202

    Homology, Гомологія, Гомология
    #Homology, #Гомологія, #Гомология
    t.me/scilib_yura15cbx/201

    Algebraic geometry
    Алгебраическая геометрия, Алгебраїчна геометрія
    t.me/scilib_yura15cbx/200

    Algebraic geometry
    #Algebraic geometry
    Алгебраическая геометрия, Алгебраїчна геометрія
    t.me/scilib_yura15cbx/200

    Finite groups
    Скінченні групи, Конечные группы
    t.me/scilib_yura15cbx/199

    Differential algebra
    #Differential algebra
    Дифференциальная алгебра, Диференціальна алгебра
    t.me/scilib_yura15cbx/198

    Category theory
    Теорія категорій, Теория категорий

    #statistics #topology #homology #wavelets #теория #perturbations
  22. Yuriy Karetin @[email protected] ·

    MVspa_ Stochastic processes
    Стохастические процессы, Випадкові процеси
    #Stochastic processes
    #Стохастическиепроцессы, #Випадковіпроцеси
    t.me/scilib_yura15cbx/230

    MVsa Statistics and applications
    Статистика та додатки, Статистика и приложения
    #Statistics
    t.me/scilib_yura15cbx/229

    EM_ Mechanics of elastic materials
    Механіка пружних матеріалів, Механика упругих материалов
    t.me/scilib_yura15cbx/228

    MPd_ Dynamical systems
    Динамические системы, Динамічні системи
    #Dynamical systems
    t.me/scilib_yura15cbx/227

    MNw_ Wavelets, signal processing
    Вейвлети, обробка сигналів, Вейвлеты, обработка сигналов
    #Wavelets, #signal processing
    t.me/scilib_yura15cbx/226

    MNs_ Simulations of physics
    Физические симуляции
    t.me/scilib_yura15cbx/225

    MNl_ Numerical linear algebra
    Числова лінійна алгебра, Численная линейная алгебра
    t.me/scilib_yura15cbx/224

    MNf_ Finite elements
    Конечные элементы, Скінченні елементи
    t.me/scilib_yura15cbx/223

    MNd_ Numerical calculus
    t.me/scilib_yura15cbx/222

    MDgt_ General topology
    #topology
    Общая топология, Загальна топологія
    t.me/scilib_yura15cbx/221

    MDdg_ Differential geometry
    Диференціальна геометрія, Дифференциальная геометрия
    t.me/scilib_yura15cbx/220

    MDat_ Algebraic and differential topology
    Алгебраическая и дифференциальная топология, Алгебраїчна та диференціальна топологія
    t.me/scilib_yura15cbx/219

    MCv_ Variational calculus
    Варіаційне числення, Вариационное исчисление
    t.me/scilib_yura15cbx/218

    MCta_ Tensor calculus, forms
    Тензорное исчисление, формы, Тензорне числення, форми
    t.me/scilib_yura15cbx/217

    MCsf_ Special functions
    Спеціальні функції, Специальные функции
    t.me/scilib_yura15cbx/216

    MCf_ Functional analysis
    Функциональный анализ, Функціональний аналіз
    t.me/scilib_yura15cbx/215

    MCet_ Elementary calculus textbooks
    Підручники з елементарного числення, Учебники по элементарному исчислению
    t.me/scilib_yura15cbx/214

    MCde_ Differential equations
    Дифференциальные уравнения, Диференціальні рівняння
    #Differential equations
    t.me/scilib_yura15cbx/213

    MCcf_ Continued fractions
    Суцільні дроби, Непрерывные дроби
    t.me/scilib_yura15cbx/212

    MCc_ Complex variable
    Комплексная переменная, Комплексна змінна
    t.me/scilib_yura15cbx/211

    MCat_ Advanced calculus
    t.me/scilib_yura15cbx/210

    Asymptotics, perturbations
    Асимптотика, збурення,
    Асимптотика, возмущения
    #Asymptotics, #perturbations
    #Асимптотика, #збурення,
    #Асимптотика, #возмущения
    t.me/scilib_yura15cbx/209

    Group theory, Теория групп, Теорія груп
    #Group theory, #Теориягрупп, #Теоріягруп
    t.me/scilib_yura15cbx/208

    Algebra textbooks,
    Підручники з алгебри,
    Учебники по алгебре
    t.me/scilib_yura15cbx/207

    Set theory,
    Теория множеств, Теорія множин
    #Set theory,
    #Теория множеств,
    t.me/scilib_yura15cbx/206

    Representation theory
    Теорія репрезентації, Теория представлений
    t.me/scilib_yura15cbx/205

    Quantum groups
    #Quantum groups
    Квантовые группы, Квантові групи
    t.me/scilib_yura15cbx/204

    Mathematical logic
    #Mathematical logic
    Математична логіка, Математическая логика
    t.me/scilib_yura15cbx/203

    Linear algebra
    #Linear algebra
    Линейная алгебра, Лінійна алгебра
    t.me/scilib_yura15cbx/202

    Homology, Гомологія, Гомология
    #Homology, #Гомологія, #Гомология
    t.me/scilib_yura15cbx/201

    Algebraic geometry
    Алгебраическая геометрия, Алгебраїчна геометрія
    t.me/scilib_yura15cbx/200

    Algebraic geometry
    #Algebraic geometry
    Алгебраическая геометрия, Алгебраїчна геометрія
    t.me/scilib_yura15cbx/200

    Finite groups
    Скінченні групи, Конечные группы
    t.me/scilib_yura15cbx/199

    Differential algebra
    #Differential algebra
    Дифференциальная алгебра, Диференціальна алгебра
    t.me/scilib_yura15cbx/198

    Category theory
    Теорія категорій, Теория категорий

    #statistics #topology #homology #wavelets #теория #perturbations
  23. Yuriy Karetin @[email protected] ·

    MVspa_ Stochastic processes
    Стохастические процессы, Випадкові процеси
    #Stochastic processes
    #Стохастическиепроцессы, #Випадковіпроцеси
    t.me/scilib_yura15cbx/230

    MVsa Statistics and applications
    Статистика та додатки, Статистика и приложения
    #Statistics
    t.me/scilib_yura15cbx/229

    EM_ Mechanics of elastic materials
    Механіка пружних матеріалів, Механика упругих материалов
    t.me/scilib_yura15cbx/228

    MPd_ Dynamical systems
    Динамические системы, Динамічні системи
    #Dynamical systems
    t.me/scilib_yura15cbx/227

    MNw_ Wavelets, signal processing
    Вейвлети, обробка сигналів, Вейвлеты, обработка сигналов
    #Wavelets, #signal processing
    t.me/scilib_yura15cbx/226

    MNs_ Simulations of physics
    Физические симуляции
    t.me/scilib_yura15cbx/225

    MNl_ Numerical linear algebra
    Числова лінійна алгебра, Численная линейная алгебра
    t.me/scilib_yura15cbx/224

    MNf_ Finite elements
    Конечные элементы, Скінченні елементи
    t.me/scilib_yura15cbx/223

    MNd_ Numerical calculus
    t.me/scilib_yura15cbx/222

    MDgt_ General topology
    #topology
    Общая топология, Загальна топологія
    t.me/scilib_yura15cbx/221

    MDdg_ Differential geometry
    Диференціальна геометрія, Дифференциальная геометрия
    t.me/scilib_yura15cbx/220

    MDat_ Algebraic and differential topology
    Алгебраическая и дифференциальная топология, Алгебраїчна та диференціальна топологія
    t.me/scilib_yura15cbx/219

    MCv_ Variational calculus
    Варіаційне числення, Вариационное исчисление
    t.me/scilib_yura15cbx/218

    MCta_ Tensor calculus, forms
    Тензорное исчисление, формы, Тензорне числення, форми
    t.me/scilib_yura15cbx/217

    MCsf_ Special functions
    Спеціальні функції, Специальные функции
    t.me/scilib_yura15cbx/216

    MCf_ Functional analysis
    Функциональный анализ, Функціональний аналіз
    t.me/scilib_yura15cbx/215

    MCet_ Elementary calculus textbooks
    Підручники з елементарного числення, Учебники по элементарному исчислению
    t.me/scilib_yura15cbx/214

    MCde_ Differential equations
    Дифференциальные уравнения, Диференціальні рівняння
    #Differential equations
    t.me/scilib_yura15cbx/213

    MCcf_ Continued fractions
    Суцільні дроби, Непрерывные дроби
    t.me/scilib_yura15cbx/212

    MCc_ Complex variable
    Комплексная переменная, Комплексна змінна
    t.me/scilib_yura15cbx/211

    MCat_ Advanced calculus
    t.me/scilib_yura15cbx/210

    Asymptotics, perturbations
    Асимптотика, збурення,
    Асимптотика, возмущения
    #Asymptotics, #perturbations
    #Асимптотика, #збурення,
    #Асимптотика, #возмущения
    t.me/scilib_yura15cbx/209

    Group theory, Теория групп, Теорія груп
    #Group theory, #Теориягрупп, #Теоріягруп
    t.me/scilib_yura15cbx/208

    Algebra textbooks,
    Підручники з алгебри,
    Учебники по алгебре
    t.me/scilib_yura15cbx/207

    Set theory,
    Теория множеств, Теорія множин
    #Set theory,
    #Теория множеств,
    t.me/scilib_yura15cbx/206

    Representation theory
    Теорія репрезентації, Теория представлений
    t.me/scilib_yura15cbx/205

    Quantum groups
    #Quantum groups
    Квантовые группы, Квантові групи
    t.me/scilib_yura15cbx/204

    Mathematical logic
    #Mathematical logic
    Математична логіка, Математическая логика
    t.me/scilib_yura15cbx/203

    Linear algebra
    #Linear algebra
    Линейная алгебра, Лінійна алгебра
    t.me/scilib_yura15cbx/202

    Homology, Гомологія, Гомология
    #Homology, #Гомологія, #Гомология
    t.me/scilib_yura15cbx/201

    Algebraic geometry
    Алгебраическая геометрия, Алгебраїчна геометрія
    t.me/scilib_yura15cbx/200

    Algebraic geometry
    #Algebraic geometry
    Алгебраическая геометрия, Алгебраїчна геометрія
    t.me/scilib_yura15cbx/200

    Finite groups
    Скінченні групи, Конечные группы
    t.me/scilib_yura15cbx/199

    Differential algebra
    #Differential algebra
    Дифференциальная алгебра, Диференціальна алгебра
    t.me/scilib_yura15cbx/198

    Category theory
    Теорія категорій, Теория категорий

    #statistics #topology #homology #wavelets #теория #perturbations
  24. Yuriy Karetin @[email protected] ·

    MVspa_ Stochastic processes
    Стохастические процессы, Випадкові процеси
    #Stochastic processes
    #Стохастическиепроцессы, #Випадковіпроцеси
    t.me/scilib_yura15cbx/230

    MVsa Statistics and applications
    Статистика та додатки, Статистика и приложения
    #Statistics
    t.me/scilib_yura15cbx/229

    EM_ Mechanics of elastic materials
    Механіка пружних матеріалів, Механика упругих материалов
    t.me/scilib_yura15cbx/228

    MPd_ Dynamical systems
    Динамические системы, Динамічні системи
    #Dynamical systems
    t.me/scilib_yura15cbx/227

    MNw_ Wavelets, signal processing
    Вейвлети, обробка сигналів, Вейвлеты, обработка сигналов
    #Wavelets, #signal processing
    t.me/scilib_yura15cbx/226

    MNs_ Simulations of physics
    Физические симуляции
    t.me/scilib_yura15cbx/225

    MNl_ Numerical linear algebra
    Числова лінійна алгебра, Численная линейная алгебра
    t.me/scilib_yura15cbx/224

    MNf_ Finite elements
    Конечные элементы, Скінченні елементи
    t.me/scilib_yura15cbx/223

    MNd_ Numerical calculus
    t.me/scilib_yura15cbx/222

    MDgt_ General topology
    #topology
    Общая топология, Загальна топологія
    t.me/scilib_yura15cbx/221

    MDdg_ Differential geometry
    Диференціальна геометрія, Дифференциальная геометрия
    t.me/scilib_yura15cbx/220

    MDat_ Algebraic and differential topology
    Алгебраическая и дифференциальная топология, Алгебраїчна та диференціальна топологія
    t.me/scilib_yura15cbx/219

    MCv_ Variational calculus
    Варіаційне числення, Вариационное исчисление
    t.me/scilib_yura15cbx/218

    MCta_ Tensor calculus, forms
    Тензорное исчисление, формы, Тензорне числення, форми
    t.me/scilib_yura15cbx/217

    MCsf_ Special functions
    Спеціальні функції, Специальные функции
    t.me/scilib_yura15cbx/216

    MCf_ Functional analysis
    Функциональный анализ, Функціональний аналіз
    t.me/scilib_yura15cbx/215

    MCet_ Elementary calculus textbooks
    Підручники з елементарного числення, Учебники по элементарному исчислению
    t.me/scilib_yura15cbx/214

    MCde_ Differential equations
    Дифференциальные уравнения, Диференціальні рівняння
    #Differential equations
    t.me/scilib_yura15cbx/213

    MCcf_ Continued fractions
    Суцільні дроби, Непрерывные дроби
    t.me/scilib_yura15cbx/212

    MCc_ Complex variable
    Комплексная переменная, Комплексна змінна
    t.me/scilib_yura15cbx/211

    MCat_ Advanced calculus
    t.me/scilib_yura15cbx/210

    Asymptotics, perturbations
    Асимптотика, збурення,
    Асимптотика, возмущения
    #Asymptotics, #perturbations
    #Асимптотика, #збурення,
    #Асимптотика, #возмущения
    t.me/scilib_yura15cbx/209

    Group theory, Теория групп, Теорія груп
    #Group theory, #Теориягрупп, #Теоріягруп
    t.me/scilib_yura15cbx/208

    Algebra textbooks,
    Підручники з алгебри,
    Учебники по алгебре
    t.me/scilib_yura15cbx/207

    Set theory,
    Теория множеств, Теорія множин
    #Set theory,
    #Теория множеств,
    t.me/scilib_yura15cbx/206

    Representation theory
    Теорія репрезентації, Теория представлений
    t.me/scilib_yura15cbx/205

    Quantum groups
    #Quantum groups
    Квантовые группы, Квантові групи
    t.me/scilib_yura15cbx/204

    Mathematical logic
    #Mathematical logic
    Математична логіка, Математическая логика
    t.me/scilib_yura15cbx/203

    Linear algebra
    #Linear algebra
    Линейная алгебра, Лінійна алгебра
    t.me/scilib_yura15cbx/202

    Homology, Гомологія, Гомология
    #Homology, #Гомологія, #Гомология
    t.me/scilib_yura15cbx/201

    Algebraic geometry
    Алгебраическая геометрия, Алгебраїчна геометрія
    t.me/scilib_yura15cbx/200

    Algebraic geometry
    #Algebraic geometry
    Алгебраическая геометрия, Алгебраїчна геометрія
    t.me/scilib_yura15cbx/200

    Finite groups
    Скінченні групи, Конечные группы
    t.me/scilib_yura15cbx/199

    Differential algebra
    #Differential algebra
    Дифференциальная алгебра, Диференціальна алгебра
    t.me/scilib_yura15cbx/198

    Category theory
    Теорія категорій, Теория категорий

    #statistics #topology #homology #wavelets #теория #perturbations
  25. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Rank of a Matrix:** Max number of linearly independent columns (or rows).
    Ex: `A=[[1,2],[0,1]]` has `rank=2`.
    Pro-Tip: If `rank(A)` = num columns, `Ax=0` only has trivial solution! Essential for unique solutions.
    #LinearAlgebra #MatrixRank #STEM #StudyNotes

    #linearalgebra #matrixrank #stem #studynotes
  26. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Rank of a Matrix:** Max number of linearly independent columns (or rows).
    Ex: `A=[[1,2],[0,1]]` has `rank=2`.
    Pro-Tip: If `rank(A)` = num columns, `Ax=0` only has trivial solution! Essential for unique solutions.
    #LinearAlgebra #MatrixRank #STEM #StudyNotes

    #linearalgebra #matrixrank #stem #studynotes
  27. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Symmetric Matrix:** A square matrix equal to its own transpose (A = A^T).
    Ex: `[[1,2],[2,3]]` is symmetric.
    Pro-Tip: They always have real eigenvalues and orthogonal eigenvectors! Important for stability & optimization.
    #MatrixProperties #LinearAlgebra #STEM #StudyNotes

    #matrixproperties #linearalgebra #stem #studynotes
  28. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Symmetric Matrix:** A square matrix equal to its own transpose (A = A^T).
    Ex: `[[1,2],[2,3]]` is symmetric.
    Pro-Tip: They always have real eigenvalues and orthogonal eigenvectors! Important for stability & optimization.
    #MatrixProperties #LinearAlgebra #STEM #StudyNotes

    #matrixproperties #linearalgebra #stem #studynotes
  29. kipriyanovich @[email protected] ·

    **Determinant:** A scalar value telling us how much a matrix scales/flips space.
    Ex: For `[[a,b],[c,d]]`, `det = ad - bc`.
    Pro-Tip: `det = 0` means the matrix isn't invertible! Its columns are linearly dependent – no unique solutions!
    #LinearAlgebra #MatrixHacks #STEM #StudyNotes

    #linearalgebra #matrixhacks #stem #studynotes
  30. kipriyanovich @[email protected] ·

    **Determinant:** A scalar value telling us how much a matrix scales/flips space.
    Ex: For `[[a,b],[c,d]]`, `det = ad - bc`.
    Pro-Tip: `det = 0` means the matrix isn't invertible! Its columns are linearly dependent – no unique solutions!
    #LinearAlgebra #MatrixHacks #STEM #StudyNotes

    #linearalgebra #matrixhacks #stem #studynotes
  31. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Null Space:** All vectors 'x' that a matrix A maps to the zero vector (Ax = 0).
    Ex: For `Ax=0`, solve for `x`.
    Pro-Tip: If null space only contains `x=0`, then `Ax=b` has a unique solution!
    #LinearAlgebra #MatrixMagic #STEM #StudyNotes

    #linearalgebra #matrixmagic #stem #studynotes
  32. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Null Space:** All vectors 'x' that a matrix A maps to the zero vector (Ax = 0).
    Ex: For `Ax=0`, solve for `x`.
    Pro-Tip: If null space only contains `x=0`, then `Ax=b` has a unique solution!
    #LinearAlgebra #MatrixMagic #STEM #StudyNotes

    #linearalgebra #matrixmagic #stem #studynotes
  33. kipriyanovich @[email protected] ·

    **Linear Independence (LI):** Vectors are LI if none can be formed by scaling/adding the others.
    Ex: If `c1*v1 + c2*v2 = 0` only when `c1=c2=0`.
    Pro-Tip: LI vectors are fundamental for forming a *basis* for a vector space!
    #LinearAlgebra #VectorSpaces #STEM #StudyNotes

    #linearalgebra #vectorspaces #stem #studynotes
  34. kipriyanovich @[email protected] ·

    **Linear Independence (LI):** Vectors are LI if none can be formed by scaling/adding the others.
    Ex: If `c1*v1 + c2*v2 = 0` only when `c1=c2=0`.
    Pro-Tip: LI vectors are fundamental for forming a *basis* for a vector space!
    #LinearAlgebra #VectorSpaces #STEM #StudyNotes

    #linearalgebra #vectorspaces #stem #studynotes
  35. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Inverse Matrix:** A matrix `A_inv` that, when multiplied by `A`, yields the identity matrix `I`.
    Ex: If `A * A_inv = I`.
    Pro-Tip: Use `A_inv` to solve `Ax=b` for `x = A_inv * b`. Super powerful for system analysis!
    #LinearAlgebra #MatrixMath #STEM #StudyNotes

    #linearalgebra #matrixmath #stem #studynotes
  36. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Inverse Matrix:** A matrix `A_inv` that, when multiplied by `A`, yields the identity matrix `I`.
    Ex: If `A * A_inv = I`.
    Pro-Tip: Use `A_inv` to solve `Ax=b` for `x = A_inv * b`. Super powerful for system analysis!
    #LinearAlgebra #MatrixMath #STEM #StudyNotes

    #linearalgebra #matrixmath #stem #studynotes
  37. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Matrix Multiplication:** Combining two matrices by taking dot products of rows from the first with columns from the second.
    Ex: `(A_mxn) * (B_nxp) = (C_mxp)`
    Pro-Tip: Inner dimensions (n) MUST match! And remember, `AB ≠ BA` usually!
    #LinearAlgebra #MatrixHacks #STEM #StudyNotes

    #linearalgebra #matrixhacks #stem #studynotes
  38. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Matrix Multiplication:** Combining two matrices by taking dot products of rows from the first with columns from the second.
    Ex: `(A_mxn) * (B_nxp) = (C_mxp)`
    Pro-Tip: Inner dimensions (n) MUST match! And remember, `AB ≠ BA` usually!
    #LinearAlgebra #MatrixHacks #STEM #StudyNotes

    #linearalgebra #matrixhacks #stem #studynotes
  39. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Linear Combination:** A sum of vectors scaled by scalars.
    Ex: `c1*v1 + c2*v2` creates a new vector from `v1` & `v2`.
    Pro-Tip: Think of it as mixing vectors. It's how basis vectors build *any* vector in their space!
    #LinearAlgebra #VectorSpaces #STEM #StudyNotes

    #linearalgebra #vectorspaces #stem #studynotes
  40. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Linear Combination:** A sum of vectors scaled by scalars.
    Ex: `c1*v1 + c2*v2` creates a new vector from `v1` & `v2`.
    Pro-Tip: Think of it as mixing vectors. It's how basis vectors build *any* vector in their space!
    #LinearAlgebra #VectorSpaces #STEM #StudyNotes

    #linearalgebra #vectorspaces #stem #studynotes
  41. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Dot Product:** A scalar value indicating how much two vectors point in the same direction.
    Ex: `v · w = v1w1 + v2w2` (for 2D).
    Pro-Tip: If `v · w = 0`, the vectors are orthogonal (perpendicular)! Key for projections.
    #LinearAlgebra #VectorMath #STEM #StudyNotes

    #stem #studynotes #linearalgebra #vectormath
  42. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Dot Product:** A scalar value indicating how much two vectors point in the same direction.
    Ex: `v · w = v1w1 + v2w2` (for 2D).
    Pro-Tip: If `v · w = 0`, the vectors are orthogonal (perpendicular)! Key for projections.
    #LinearAlgebra #VectorMath #STEM #StudyNotes

    #stem #studynotes #linearalgebra #vectormath
  43. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Matrix Transpose:** Swapping a matrix's rows for its columns.
    Ex: `[[1,2],[3,4]]^T` becomes `[[1,3],[2,4]]`.
    Pro-Tip: `(AB)^T = B^T A^T`. Order matters when transposing products!
    #LinearAlgebra #MatrixHacks #STEM #StudyNotes

    #linearalgebra #matrixhacks #stem #studynotes
  44. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Matrix Transpose:** Swapping a matrix's rows for its columns.
    Ex: `[[1,2],[3,4]]^T` becomes `[[1,3],[2,4]]`.
    Pro-Tip: `(AB)^T = B^T A^T`. Order matters when transposing products!
    #LinearAlgebra #MatrixHacks #STEM #StudyNotes

    #linearalgebra #matrixhacks #stem #studynotes
  45. kipriyanovich @[email protected] ·

    Engineers!
    **Dot Product:** Measures how much two vectors point in the same direction, yielding a scalar.
    Ex: `[a,b] . [c,d] = ac + bd`.
    Pro-Tip: If `v.w = 0`, vectors `v` and `w` are perpendicular. Key for orthogonality checks!
    #LinearAlgebra #Vectors #STEM #StudyNotes

    #linearalgebra #vectors #stem #studynotes
  46. kipriyanovich @[email protected] ·

    Engineers!
    **Dot Product:** Measures how much two vectors point in the same direction, yielding a scalar.
    Ex: `[a,b] . [c,d] = ac + bd`.
    Pro-Tip: If `v.w = 0`, vectors `v` and `w` are perpendicular. Key for orthogonality checks!
    #LinearAlgebra #Vectors #STEM #StudyNotes

    #linearalgebra #vectors #stem #studynotes
  47. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Linear Transformation:** A function that maps vectors, preserving addition & scalar mult.
    Ex: `T(v) = Av` (matrix A transforms vector v).
    Pro-Tip: It 'stretches', 'rotates', or 'reflects' space. Visualize it!
    #LinearAlgebra #Vectors #STEM #StudyNotes

    #linearalgebra #vectors #stem #studynotes
  48. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Linear Transformation:** A function that maps vectors, preserving addition & scalar mult.
    Ex: `T(v) = Av` (matrix A transforms vector v).
    Pro-Tip: It 'stretches', 'rotates', or 'reflects' space. Visualize it!
    #LinearAlgebra #Vectors #STEM #StudyNotes

    #linearalgebra #vectors #stem #studynotes
  49. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Linear Independence:** Vectors are LI if no vector can be written as a combination of the others.
    Ex: `c1*v1 + c2*v2 = 0` implies `c1=c2=0`.
    Pro-Tip: LI vectors form the building blocks (basis) of a vector space. No redundancy!
    #LinearAlgebra #Vectors #STEM #StudyNotes

    #linearalgebra #vectors #stem #studynotes
  50. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Linear Independence:** Vectors are LI if no vector can be written as a combination of the others.
    Ex: `c1*v1 + c2*v2 = 0` implies `c1=c2=0`.
    Pro-Tip: LI vectors form the building blocks (basis) of a vector space. No redundancy!
    #LinearAlgebra #Vectors #STEM #StudyNotes

    #linearalgebra #vectors #stem #studynotes
  51. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Matrix Multiplication:** Combines two matrices, representing sequential linear transformations.
    Ex: An (m x n) * (n x p) matrix yields an (m x p) result.
    Pro-Tip: The number of columns in the first matrix *must* equal the rows in the second (n=n)!
    #LinearAlgebra #Matrices #STEM #StudyNotes

    #linearalgebra #matrices #stem #studynotes
  52. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Matrix Multiplication:** Combines two matrices, representing sequential linear transformations.
    Ex: An (m x n) * (n x p) matrix yields an (m x p) result.
    Pro-Tip: The number of columns in the first matrix *must* equal the rows in the second (n=n)!
    #LinearAlgebra #Matrices #STEM #StudyNotes

    #linearalgebra #matrices #stem #studynotes
  53. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Dot Product:** A scalar showing how much two vectors point in the same direction.
    Ex: `u . v = u1v1 + u2v2`
    Pro-Tip: If `u . v = 0`, vectors are orthogonal (perpendicular)! Super useful for geometry & projections.
    #LinearAlgebra #Vectors #STEM #StudyNotes

    #linearalgebra #vectors #stem #studynotes
  54. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Dot Product:** A scalar showing how much two vectors point in the same direction.
    Ex: `u . v = u1v1 + u2v2`
    Pro-Tip: If `u . v = 0`, vectors are orthogonal (perpendicular)! Super useful for geometry & projections.
    #LinearAlgebra #Vectors #STEM #StudyNotes

    #linearalgebra #vectors #stem #studynotes
  55. kipriyanovich @[email protected] ·

    **Linear Independence:** Vectors are independent if none can be formed by scaling & adding the others.
    Ex: `[1,0]` and `[0,1]` are independent.
    Pro-Tip: If the only solution to `c1v1 + c2v2 = 0` is `c1=c2=0`, your vectors are independent!
    #LinearAlgebra #Vectors #STEM #StudyNotes

    #linearalgebra #vectors #stem #studynotes
  56. kipriyanovich @[email protected] ·

    **Linear Independence:** Vectors are independent if none can be formed by scaling & adding the others.
    Ex: `[1,0]` and `[0,1]` are independent.
    Pro-Tip: If the only solution to `c1v1 + c2v2 = 0` is `c1=c2=0`, your vectors are independent!
    #LinearAlgebra #Vectors #STEM #StudyNotes

    #linearalgebra #vectors #stem #studynotes
  57. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Matrix:** A rectangular grid of numbers organized into rows & columns.
    Ex: `A = [[1,2],[3,4]]` (2x2).
    Pro-Tip: Dimensions (rows x cols) dictate *all* operations! Check `(m x n)` first!
    #LinearAlgebra #Matrices #STEM #StudyNotes

    #linearalgebra #matrices #stem #studynotes
  58. kipriyanovich @[email protected] ·

    Alright, future engineers!
    **Matrix:** A rectangular grid of numbers organized into rows & columns.
    Ex: `A = [[1,2],[3,4]]` (2x2).
    Pro-Tip: Dimensions (rows x cols) dictate *all* operations! Check `(m x n)` first!
    #LinearAlgebra #Matrices #STEM #StudyNotes

    #linearalgebra #matrices #stem #studynotes