#linearalgebra — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #linearalgebra, aggregated by home.social.
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#Python for all your #linearalgebra homework:
#!/usr/bin/env python3
import sys,ast,numpy as np
a=np.array(ast.literal_eval(sys.argv[1]))
print("Matrix:")
print(np.matrix(a))
print("\nTranspose:")
print(np.matrix(a.T))
print("\nTrace:",a.trace())
print("\nRank:",np.linalg.matrix_rank(a))
if a.shape[0]==a.shape[1]:
print("\nDeterminant:",round(np.linalg.det(a),6))
d,e=np.linalg.eig(a)
print("\nEigenvalues:",np.round(d,6))
print("\nEigenvectors:")
print(np.round(e,6))
print("\nPseudo-inverse:")
print(np.matrix(np.linalg.pinv(a))) -
Alright, future engineers!
The **Dot Product** takes two vectors and returns a scalar. It tells you how much they align!
Ex: For `v=[v1,v2]` & `w=[w1,w2]`, `v.w = v1w1 + v2w2`.
Pro-Tip: If `v.w = 0`, the vectors are orthogonal (perpendicular)!
#LinearAlgebra #Vectors #STEM #StudyNotes -
Alright, future engineers!
The **Dot Product** takes two vectors and returns a scalar. It tells you how much they align!
Ex: For `v=[v1,v2]` & `w=[w1,w2]`, `v.w = v1w1 + v2w2`.
Pro-Tip: If `v.w = 0`, the vectors are orthogonal (perpendicular)!
#LinearAlgebra #Vectors #STEM #StudyNotes -
Alright, future engineers!
The **Dot Product** takes two vectors and returns a scalar. It tells you how much they align!
Ex: For `v=[v1,v2]` & `w=[w1,w2]`, `v.w = v1w1 + v2w2`.
Pro-Tip: If `v.w = 0`, the vectors are orthogonal (perpendicular)!
#LinearAlgebra #Vectors #STEM #StudyNotes -
Alright, future engineers!
The **Dot Product** takes two vectors and returns a scalar. It tells you how much they align!
Ex: For `v=[v1,v2]` & `w=[w1,w2]`, `v.w = v1w1 + v2w2`.
Pro-Tip: If `v.w = 0`, the vectors are orthogonal (perpendicular)!
#LinearAlgebra #Vectors #STEM #StudyNotes -
Alright, future engineers!
The **Dot Product** takes two vectors and returns a scalar. It tells you how much they align!
Ex: For `v=[v1,v2]` & `w=[w1,w2]`, `v.w = v1w1 + v2w2`.
Pro-Tip: If `v.w = 0`, the vectors are orthogonal (perpendicular)!
#LinearAlgebra #Vectors #STEM #StudyNotes -
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!
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!
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!
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!
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** 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** 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** 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** 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!
The **Dot Product** of two vectors gives a scalar, measuring their alignment.
Ex: For `v=[1,2]`, `w=[3,4]`, `v.w = (1*3) + (2*4) = 11`.
Pro-Tip: A zero dot product means the vectors are orthogonal! -
Alright, future engineers!
The **Dot Product** of two vectors gives a scalar, measuring their alignment.
Ex: For `v=[1,2]`, `w=[3,4]`, `v.w = (1*3) + (2*4) = 11`.
Pro-Tip: A zero dot product means the vectors are orthogonal! -
Alright, future engineers!
The **Dot Product** of two vectors gives a scalar, measuring their alignment.
Ex: For `v=[1,2]`, `w=[3,4]`, `v.w = (1*3) + (2*4) = 11`.
Pro-Tip: A zero dot product means the vectors are orthogonal! -
Alright, future engineers!
The **Dot Product** of two vectors gives a scalar, measuring their alignment.
Ex: For `v=[1,2]`, `w=[3,4]`, `v.w = (1*3) + (2*4) = 11`.
Pro-Tip: A zero dot product means the vectors are orthogonal! -
Alright, future engineers!
The **Dot Product** of two vectors gives a scalar, measuring their alignment.
Ex: For `v=[1,2]`, `w=[3,4]`, `v.w = (1*3) + (2*4) = 11`.
Pro-Tip: A zero dot product means the vectors are orthogonal! -
OH "Most programmers will go far, far, far out of their way with trigonometry and complex loops to avoid having to learn basic #linearalgebra things."
-
OH "Most programmers will go far, far, far out of their way with trigonometry and complex loops to avoid having to learn basic #linearalgebra things."
-
OH "Most programmers will go far, far, far out of their way with trigonometry and complex loops to avoid having to learn basic #linearalgebra things."
-
OH "Most programmers will go far, far, far out of their way with trigonometry and complex loops to avoid having to learn basic #linearalgebra things."
-
OH "Most programmers will go far, far, far out of their way with trigonometry and complex loops to avoid having to learn basic #linearalgebra things."
-
Alright, future engineers!
The **Norm** (`||v||`) is the length or magnitude of a vector. Ex: For `v=[3,4]`, `||v|| = sqrt(3^2 + 4^2) = 5`. Pro-Tip: Essential for calculating distances & normalizing vectors to unit length!
#LinearAlgebra #VectorMath #STEM #StudyNotes -
Alright, future engineers!
The **Norm** (`||v||`) is the length or magnitude of a vector. Ex: For `v=[3,4]`, `||v|| = sqrt(3^2 + 4^2) = 5`. Pro-Tip: Essential for calculating distances & normalizing vectors to unit length!
#LinearAlgebra #VectorMath #STEM #StudyNotes -
Alright, future engineers!
The **Norm** (`||v||`) is the length or magnitude of a vector. Ex: For `v=[3,4]`, `||v|| = sqrt(3^2 + 4^2) = 5`. Pro-Tip: Essential for calculating distances & normalizing vectors to unit length!
#LinearAlgebra #VectorMath #STEM #StudyNotes -
Alright, future engineers!
The **Norm** (`||v||`) is the length or magnitude of a vector. Ex: For `v=[3,4]`, `||v|| = sqrt(3^2 + 4^2) = 5`. Pro-Tip: Essential for calculating distances & normalizing vectors to unit length!
#LinearAlgebra #VectorMath #STEM #StudyNotes -
Alright, future engineers!
The **Norm** (`||v||`) is the length or magnitude of a vector. Ex: For `v=[3,4]`, `||v|| = sqrt(3^2 + 4^2) = 5`. Pro-Tip: Essential for calculating distances & normalizing vectors to unit length!
#LinearAlgebra #VectorMath #STEM #StudyNotes -
Alright, future engineers!
The **Identity Matrix (I)** is a square matrix with 1s on the main diagonal & 0s elsewhere.
Ex: For 2x2, `I = [[1,0],[0,1]]`.
Pro-Tip: It's the 1 of matrix multiplication – `AI = IA = A`. Essential for inverses!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
The **Identity Matrix (I)** is a square matrix with 1s on the main diagonal & 0s elsewhere.
Ex: For 2x2, `I = [[1,0],[0,1]]`.
Pro-Tip: It's the 1 of matrix multiplication – `AI = IA = A`. Essential for inverses!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
The **Identity Matrix (I)** is a square matrix with 1s on the main diagonal & 0s elsewhere.
Ex: For 2x2, `I = [[1,0],[0,1]]`.
Pro-Tip: It's the 1 of matrix multiplication – `AI = IA = A`. Essential for inverses!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
The **Identity Matrix (I)** is a square matrix with 1s on the main diagonal & 0s elsewhere.
Ex: For 2x2, `I = [[1,0],[0,1]]`.
Pro-Tip: It's the 1 of matrix multiplication – `AI = IA = A`. Essential for inverses!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
The **Identity Matrix (I)** is a square matrix with 1s on the main diagonal & 0s elsewhere.
Ex: For 2x2, `I = [[1,0],[0,1]]`.
Pro-Tip: It's the 1 of matrix multiplication – `AI = IA = A`. Essential for inverses!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication** combines two matrices `A` & `B` into `C=AB`. Each `C_ij` is `(Row i of A) . (Col j of B)`.
Ex: `(m x n)` times `(n x p)` gives `(m x p)`. Inner dimensions `n` must match!
Pro-Tip: Order matters! `AB` is rarely equal to `BA` (not commutative).
#LinearAlgebra #MatrixOps #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication** combines two matrices `A` & `B` into `C=AB`. Each `C_ij` is `(Row i of A) . (Col j of B)`.
Ex: `(m x n)` times `(n x p)` gives `(m x p)`. Inner dimensions `n` must match!
Pro-Tip: Order matters! `AB` is rarely equal to `BA` (not commutative).
#LinearAlgebra #MatrixOps #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication** combines two matrices `A` & `B` into `C=AB`. Each `C_ij` is `(Row i of A) . (Col j of B)`.
Ex: `(m x n)` times `(n x p)` gives `(m x p)`. Inner dimensions `n` must match!
Pro-Tip: Order matters! `AB` is rarely equal to `BA` (not commutative).
#LinearAlgebra #MatrixOps #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication** combines two matrices `A` & `B` into `C=AB`. Each `C_ij` is `(Row i of A) . (Col j of B)`.
Ex: `(m x n)` times `(n x p)` gives `(m x p)`. Inner dimensions `n` must match!
Pro-Tip: Order matters! `AB` is rarely equal to `BA` (not commutative).
#LinearAlgebra #MatrixOps #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication** combines two matrices `A` & `B` into `C=AB`. Each `C_ij` is `(Row i of A) . (Col j of B)`.
Ex: `(m x n)` times `(n x p)` gives `(m x p)`. Inner dimensions `n` must match!
Pro-Tip: Order matters! `AB` is rarely equal to `BA` (not commutative).
#LinearAlgebra #MatrixOps #STEM #StudyNotes -
Alright, future engineers!
A **Determinant** is a scalar value that provides properties of a square matrix (e.g., if it's invertible).
Ex: For `A = [[a,b],[c,d]]`, `det(A) = ad - bc`.
Pro-Tip: If `det(A) = 0`, the matrix is singular (no inverse)! -
Alright, future engineers!
A **Determinant** is a scalar value that provides properties of a square matrix (e.g., if it's invertible).
Ex: For `A = [[a,b],[c,d]]`, `det(A) = ad - bc`.
Pro-Tip: If `det(A) = 0`, the matrix is singular (no inverse)! -
Alright, future engineers!
A **Determinant** is a scalar value that provides properties of a square matrix (e.g., if it's invertible).
Ex: For `A = [[a,b],[c,d]]`, `det(A) = ad - bc`.
Pro-Tip: If `det(A) = 0`, the matrix is singular (no inverse)! -
Alright, future engineers!
A **Determinant** is a scalar value that provides properties of a square matrix (e.g., if it's invertible).
Ex: For `A = [[a,b],[c,d]]`, `det(A) = ad - bc`.
Pro-Tip: If `det(A) = 0`, the matrix is singular (no inverse)!
