This project demonstrates how to perform QR, LU, and Cholesky decompositions on symmetric positive definite (SPD) matrices using the Eigen library in C++. It measures the average time taken for each decomposition method and provides a comparison of their performance.

• Introduction
• Decomposition Details
• Performance Measurement

This project defines a MatrixDecomposer class that performs matrix decompositions on randomly generated symmetric positive definite (SPD) matrices. It showcases three decomposition techniques:

• QR Decomposition
• LU Decomposition
• Cholesky Decomposition

• QR Decomposition: Factorizes a matrix into a product of an orthogonal matrix (Q) and an upper triangular matrix (R).
• LU Decomposition: Decomposes a matrix into a product of a lower triangular matrix (L) and an upper triangular matrix (U).
• Cholesky Decomposition: Performs a specialized LU decomposition for symmetric positive definite matrices, resulting in a lower triangular matrix (L).

The program measures the average time taken for each decomposition method over a fixed number of iterations (10 by default). The performance results are displayed as:

• Average QR Decomposition Time
• Average LU Decomposition Time
• Average Cholesky Decomposition Time
• The ratios of the times taken by QR, LU, and Cholesky decompositions are also displayed for comparison.