SCIPK
← ABOUT · HIGHLIGHTED COURSES
MATH-543 · SP26 · NUMERICAL MATRIX ANALYSIS · MATLAB

Numerical Matrix Analysis

San Diego State University, Spring 2026. Taught by Dr. Peter Blomgren.

LINEAR ALGEBRASVDEIGENVALUE PROBLEMSQR ALGORITHMMATLAB

Problem

This course explores the mathematical foundations and computational techniques of matrix analysis, covering decomposition methods (SVD, LU, Cholesky), orthogonalization and QR factorization, linear system conditioning and numerical stability, Gaussian elimination with pivoting strategies, eigenvalue computation through iterative diagonalization, and advanced matrix transformations including tridiagonal, Hessenberg, and Householder matrices, culminating in the QR algorithm.

Numerical matrix analysis
FIG. 1 — NUMERICAL MATRIX ANALYSIS

Approach

This class used MATLAB for numerical computations. I chose to use LaTeX to write my homework.

DECOMPOSESVD, LU, Cholesky, and QR factorization of the system matrix.
CONDITIONAssess conditioning and numerical stability before trusting a solve.
ITERATEHouseholder and Hessenberg reduction into the QR algorithm for eigenvalues.
SINGULAR VALUE DECOMPOSITIONEQ. 1
A = U Σ Vᵀ
κ(A) = σ_max / σ_min
The same decomposition underwrites observability and controllability analysis, least-squares state estimation, and the conditioning checks that say whether a GNC solve can be believed.

My Contribution

COURSEWORK

All eight homework sets are my own work: the MATLAB implementations of the algorithms above, written up in LaTeX. The repository holds the LaTeX sources and the MATLAB scripts.

Result

The homework sets below are the artifact — each one carries the MATLAB code for that unit’s numerical methods alongside the derivation.

Homework 1Homework 2Homework 3Homework 4Homework 5Homework 6Homework 7Homework 8

Code

All LaTeX source code, MATLAB scripts, and project files are available on GitHub. The repository includes the complete LaTeX documentation for all lab reports and data analysis scripts used throughout the course.

GITHUB REPOSITORYscipk/MATH-543-SDSUVIEW REPOSITORY →