Linear algebra in python

Number of operations and problems in Linear Algebra and Numerical Linear Algebra

List of items

01. Matrix operations:

Addition
Subtraction
Division
Multiplication
Dot product (Scalar product)
Inner product
Outer product
Determinant
Rank
Square root
Summation of elements
Column wise summation
Row wise summation
Matrix transposition
Inverse
Eigenvalues
Eigenvectors

02. Some of above operation without NumPy

03. Cramer's rule

04. Matrix norms:

L¹ norm
L² norm
Squared L² norm
Max norm
Euclidean distance
Frobenius norm & Condition number

05. Five inequalities:

details in 05-inequality-details.pdf

06. LU and PLU decomposition

07. Determinant using LU and PLU decomposition (Gaussian Elimination)

08. solve `Ax=b` equations with LU decomposition(gaussian_elimination)

09. Householder matrix

10. QR decomposition using Householder

11. Cholesky decomposition

12. Checking for Positive definite matrix

13. Jacobi method

14. Gauss Seidel method

15. Checking for Diagonally dominant matrix

16. Power method (Largest eigenvalues and eigenvector)

Name		Name	Last commit message	Last commit date
Latest commit History 4 Commits
01-matrixOperation.py		01-matrixOperation.py
02-matrixOperation(not_numpy).py		02-matrixOperation(not_numpy).py
03-cramer_rule.py		03-cramer_rule.py
04-norms.py		04-norms.py
05-inequality-details.pdf		05-inequality-details.pdf
05-inequality.py		05-inequality.py
06-lu_and_plu_decompositions.py		06-lu_and_plu_decompositions.py
07-determinant_using_lu_and_plu_decomposition(gaussian_elimination).py		07-determinant_using_lu_and_plu_decomposition(gaussian_elimination).py
08-solve_Ax=b_equations_with_lu_decomposition(gaussian_elimination).py		08-solve_Ax=b_equations_with_lu_decomposition(gaussian_elimination).py
09-householder_matrix.py		09-householder_matrix.py
10-qr_decomposition_using_householder.py		10-qr_decomposition_using_householder.py
11-cholesky_decomposition.py		11-cholesky_decomposition.py
12-positive_definite_matrix_check.py		12-positive_definite_matrix_check.py
13-jacobi_method.py		13-jacobi_method.py
14-gauss_Seidel_method.py		14-gauss_Seidel_method.py
15-diagonally_dominant_matrix_check.py		15-diagonally_dominant_matrix_check.py
16-power_method(largest_eigenvalues_and _eigenvector).py		16-power_method(largest_eigenvalues_and _eigenvector).py
README.md		README.md

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Linear algebra in python

List of items

01. Matrix operations:

02. Some of above operation without NumPy

03. Cramer's rule

04. Matrix norms:

05. Five inequalities:

06. LU and PLU decomposition

07. Determinant using LU and PLU decomposition (Gaussian Elimination)

08. solve Ax=b equations with LU decomposition(gaussian_elimination)

09. Householder matrix

10. QR decomposition using Householder

11. Cholesky decomposition

12. Checking for Positive definite matrix

13. Jacobi method

14. Gauss Seidel method

15. Checking for Diagonally dominant matrix

16. Power method (Largest eigenvalues and eigenvector)

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08. solve `Ax=b` equations with LU decomposition(gaussian_elimination)