algebra implementation

Linear algebra algorithms with efficient implementations, available for different types of problems.

P1: Echelon Form

This project gets a square matrix (A) and a vector (b) then:

1. Transforming matrix to Row Echelon form (show results step by step).
2. Transforming Row Echelon matrix to reduced Row Echelon form (show results step by step)
3. Solving Ax=b equation which A is a n * n matrix and b is a vector in Rⁿ

P2: Inveret a matrix by LU decomposition

In this project, LU decomposition is used to calculate the inverted matrix efficiently. It contains:

1. forward-substitution function for calculating L matrix
2. backward-substitution function for calculating U matrix
3. LU decomposition function, which speeds up our calculation to solve Ax=b equation

solve AX = I by LU decomposition to find the Inverted matrix.

P3: Vector space

This project takes a matrix as input and extracts the row, column, and Nullspace basis of the matrix using reduced Echelon form.

P4: Linear Regression

This project predict COVID-19-infected number by Linear regression and curve fitting. you can download the total_cases.csv file from here.

P5: Image compresseion

The singular value decomposition (SVD) is a factorization of a real or complex matrix that generalizes the eigen decomposition of a normal square matrix to any m*n matrix. Here we use it to compress a .PPM photo and plot it a lower resolution