alirezafarzipour/linear_algebra_python

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)