MATLAB/Octave Scientific Computing

MATLAB is a numerical computing environment optimized for matrix operations and scientific computing. GNU Octave is a free, open-source alternative with high MATLAB compatibility.

Quick Start

Running MATLAB scripts:

# MATLAB (commercial)
matlab -nodisplay -nosplash -r "run('script.m'); exit;"

# GNU Octave (free, open-source)
octave script.m

Install GNU Octave:

# macOS
brew install octave

# Ubuntu/Debian
sudo apt install octave

# Windows - download from https://octave.org/download

Core Capabilities

1. Matrix Operations

MATLAB operates fundamentally on matrices and arrays:

% Create matrices
A = [1 2 3; 4 5 6; 7 8 9];  % 3x3 matrix
v = 1:10;                     % Row vector 1 to 10
v = linspace(0, 1, 100);      % 100 points from 0 to 1

% Special matrices
I = eye(3);          % Identity matrix
Z = zeros(3, 4);     % 3x4 zero matrix
O = ones(2, 3);      % 2x3 ones matrix
R = rand(3, 3);      % Random uniform
N = randn(3, 3);     % Random normal

% Matrix operations
B = A';              % Transpose
C = A * B;           % Matrix multiplication
D = A .* B;          % Element-wise multiplication
E = A \ b;           % Solve linear system Ax = b
F = inv(A);          % Matrix inverse

For complete matrix operations, see references/matrices-arrays.md.

2. Linear Algebra

% Eigenvalues and eigenvectors
[V, D] = eig(A);     % V: eigenvectors, D: diagonal eigenvalues

% Singular value decomposition
[U, S, V] = svd(A);

% Matrix decompositions
[L, U] = lu(A);      % LU decomposition
[Q, R] = qr(A);      % QR decomposition
R = chol(A);         % Cholesky (symmetric positive definite)

% Solve linear systems
x = A \ b;           % Preferred method
x = linsolve(A, b);  % With options
x = inv(A) * b;      % Less efficient

For comprehensive linear algebra, see references/mathematics.md.