Matrix Calculus

This repository hosts programs developed for the "Matrix Calculus and Multivariate Statistics" course at AGH University during the academic year 2023/2024. The programms are written along with paula078.

Program 1: Matrix Multiplication Methods Implementation

Objective:

The primary objective of this program is to implement two distinct matrix multiplication methods:

• Classic Matrix Multiplication
• Binet Matrix Multiplication

Methodology:

The program further incorporates an algorithm that bridges these two approaches. Initially, it divides the given matrices recursively into block matrices. These blocks, starting from a designated parameter "l", are then multiplied using the traditional method and subsequently reassembled.

Evaluation:

The program assesses the performance by comparing the execution time and floating-point operations per second for various "l" parameters.

Assumption: The program operates on square matrices with sizes that are powers of two.

Program 2: Gaussian Elimination and LU Factorization

Objective:

This program aims to implement efficient solutions for solving systems of linear equations by incorporating the following techniques:

• Gaussian elimination (with and without pivoting)
• LU factorization (with and without pivoting)

Program 3: Matrix Norms and Singular Value Decomposition

Objective:

This program calculates various matrix norms, matrix condition numbers, and also performs singular value decomposition: