1. SVD :

Calculation of Singular Value Decomposition (SVD) of Matrix -
calculat Eigenvalues and Eigenvectors of matrix by Jacobi Method.
And then, calculat the of the given matrix.

2. QR Decomposition - Using Gram–Schmidt process:

Perform Gram–Schmidt process on the matrix and get matrix called .
Create matrix by normalize the columns of .
Create matrix by execute which is the dot product between matrix and input matrix called .

Implementing of the project has been done in C++ and Python :

C++ :

The Class Diagram of the C++ project is located Here.
Project application : Matrix_Decomposition.exe.
C++ Source Code and Header Files is located Here.
C++ Project main files are:
Matrix_Operations.cpp - contain various methods for all the required operations that can been done on matrices.
Jacobi.cpp - contain methods for Jacobi eigenvalue algorithm and methods for calculating matrices.
QR_Decomposition.cpp - contain methods for calculating QR decomposition.
Project_main.cpp - the main method.
LU Decomposition - contain project that calculating LU decomposition.\

Python :