MATLAB Scripts for MA1508E

This repository contains a collection of MATLAB scripts developed for MA1508E (Linear Algebra for Engineering).

⚠️ These scripts may not be entirely error-free. Use with caution.

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Files Included

File	Description
Eigenvalue.m	Computes eigenvalues and display all necessary steps
GeneraliseEigenvalue.m	Handles generalized eigenvectors and display all necessary steps
orthogonalize.m	Applies Gram-Schmidt for orthogonal basis
orthonormal.m	Applies Gram-Schmidt and normalizes to an orthonormal basis
least_square_solution.m	Solves least squares
projection.m	Projects a vector onto a matrix's column space
solve_linear_system.m	Solves symbolic linear ODE systems

Usage

These functions are best used inside MATLAB Live Scripts for step-by-step output.

Add the Folder to Your MATLAB Path

In the Command Window, run:

% Add the folder containing the scripts to your MATLAB path:
addpath("path/to/your/folder");

% (Optional) Save the path for future sessions:
savepath;

Function Calls (Use in Live Script)

⚠️ Step-by-step output only displays in Live Scripts (not in Command Window)

% Compute eigenvalues and eigenvectors (with step-by-step display)
A = [2 1; 1 2];
[P, D] = Eigenvalue(A);

% Find generalized eigenvectors for non-diagonalizable matrices
A = [4 1; 0 4];
GeneraliseEigenvalue(A);

% Apply Gram-Schmidt for orthogonal basis
U = [1 1; 1 -1; 1 2];
V = orthogonalize(U);

% Apply Gram-Schmidt and normalize to orthonormal basis
V = orthonormal(U);

% Solve least squares problem A * x ≈ w
A = [1 1; 1 -1; 1 2];
w = [2; 0; 3];
x = least_square_solution(A, w);

% Project vector w onto the column space of A
wp = projection(A, w);

% Solve the system dy/dt = A*y with initial condition y(0) = y0
A = [0 1; -2 -3];
y0 = [1; 0];
solve_linear_system(A, y0);