#matrices — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #matrices, aggregated by home.social.
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Alright, future engineers!
The **Determinant** of a square matrix is a scalar value that tells you if the matrix is invertible.
Ex: For `[[a,b],[c,d]]`, `det = ad - bc`.
Pro-Tip: If `det = 0`, the matrix is singular (no inverse), meaning `Ax=b` has no unique solution! -
Alright, future engineers!
**Matrix multiplication** combines two matrices, forming a new one where elements are dot products of rows & columns.
Ex: `(AB)_ij = sum(A_ik * B_kj)`. Inner dimensions must match!
Pro-Tip: It's NOT commutative (AB != BA)!
#Matrices #LinearAlgebra #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication** creates a new matrix where `C_ij` is the dot product of row `i` from the 1st matrix & column `j` from the 2nd.
Ex: `A(2x3) * B(3x2)` gives `C(2x2)`.
Pro-Tip: Inner dimensions must match! -
🎩🤓 Behold, the blog that bravely attempts to explain the mystical Q, K, V #matrices as if they're the holy trinity of #AI. Spoiler alert: it's mostly a glorified game of 'which word matters?' because we all need another reason to overcomplicate common sense. 🙄🔍
https://arpitbhayani.me/blogs/qkv-matrices/ #QKV #Overcomplication #CommonSense #HackerNews #HackerNews #ngated -
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#Matriceshttps://www.meta.com/experiences/app/8875714305775804/?utm_source=oculus&utm_medium=share
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Pour s'amuser avec les matrices et #geogebra: 3 exemples pour générer des motifs aléatoires de Truchet.
https://www.geogebra.org/m/hap9nyjs#chapter/1127720
#matrix #maths #teaching #TeachingMaths #matrices #MathsExpertes
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For all Transf ∈ ℝn×n, the matrix is invertible if and only if rank(Transf) = n
The #determinant exists if and only if the transformation matrix is square.
The determinant in a linear transformation is the (signed) area of the image of the fundamental basis formed by the unit square.#algebra #matrices #tutorial #determinants #singularity #math #maths #mathematics #mathStodon #ML #machineLearning #systems
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#Algebra thread 🧵
Which #matrices have an inverse?
Singular matrices never have an inverse.
When we look at the determinant, the determinant is non-zero for invertible matrices in the same way that non-zero numbers have an inverse.
Non-zero determinants mean that the matrices has an inverse, and a zero determinant means that the system (of sentences, of graphs) is singular.#tutorial #learning #determinants #singularity #math #maths #mathematics #mathStodon #ML #machineLearning #systems
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Data returned by an observation typically is represented as a vector in machine learning.
A neural network can be seen as a large collection of linear models. We may represent the inputs and outputs of each layer as vectors, matrices, and tensors (which are like higher dimensional matrices).
#algebra #linearAlgebra #vectors #matrices #determinants #singularity #ML #DataScience #math #maths #mathematics #mathStodon #ML #data #dataDon #dataScience #machineLearning #DeepLearning #neuralNetworks
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Linear algebra (continued)
Which of the below operations, when applied to the rows of a matrix, keeps the #singularity (or non-singularity) of the matrix?:
(Hint: It works the same as a system of linear equations.)#learning #algebra #systems #matrices #determinants #singularity #data #ML #DataScience #math #maths #mathematics #mathStodon #tutorial #poll #exercise #exercice #puzzle #calculus
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A system (of sentences, of equations, of graphs) is said "complete" if it has one and only one solution.
A system is deemed "singular" if it does not have one and only one solution.A convenient way to show singularity is to:
* define a "determinant" as the product of the leading diagonal minus the product of the antidiagonal and
* calculate that it is zero.#learning #algebra #systems #matrices #determinants #singularity #data #ML #DataScience #math #maths #mathematics #tutorial
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#FreemanDyson - What's #Fundamental in the #Cosmos?
https://www.youtube.com/watch?v=JkNTXzsYurA
#Philosophy #PhilosophyOfScience #Science #Physics #Fundamentalism #Physicalism #Materialism #Math #Maths #Mathematics #Matrices #FFT #FastFourierTransform #RandomMatrices #QM #QuantumMechanics #QED #QuantumElectrodynamics #Gravity #QuantumGravity #GR #GeneralRelativity #CloserToTruth #RobertKuhn
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#FreemanDyson - What's #Fundamental in the #Cosmos?
https://www.youtube.com/watch?v=JkNTXzsYurA
#Philosophy #PhilosophyOfScience #Science #Physics #Fundamentalism #Physicalism #Materialism #Math #Maths #Mathematics #Matrices #FFT #FastFourierTransform #RandomMatrices #QM #QuantumMechanics #QED #QuantumElectrodynamics #Gravity #QuantumGravity #GR #GeneralRelativity #CloserToTruth #RobertKuhn
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#FreemanDyson - What's #Fundamental in the #Cosmos?
https://www.youtube.com/watch?v=JkNTXzsYurA
#Philosophy #PhilosophyOfScience #Science #Physics #Fundamentalism #Physicalism #Materialism #Math #Maths #Mathematics #Matrices #FFT #FastFourierTransform #RandomMatrices #QM #QuantumMechanics #QED #QuantumElectrodynamics #Gravity #QuantumGravity #GR #GeneralRelativity #CloserToTruth #RobertKuhn
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#FreemanDyson - What's #Fundamental in the #Cosmos?
https://www.youtube.com/watch?v=JkNTXzsYurA
#Philosophy #PhilosophyOfScience #Science #Physics #Fundamentalism #Physicalism #Materialism #Math #Maths #Mathematics #Matrices #FFT #FastFourierTransform #RandomMatrices #QM #QuantumMechanics #QED #QuantumElectrodynamics #Gravity #QuantumGravity #GR #GeneralRelativity #CloserToTruth #RobertKuhn
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#FreemanDyson - What's #Fundamental in the #Cosmos?
https://www.youtube.com/watch?v=JkNTXzsYurA
#Philosophy #PhilosophyOfScience #Science #Physics #Fundamentalism #Physicalism #Materialism #Math #Maths #Mathematics #Matrices #FFT #FastFourierTransform #RandomMatrices #QM #QuantumMechanics #QED #QuantumElectrodynamics #Gravity #QuantumGravity #GR #GeneralRelativity #CloserToTruth #RobertKuhn
