matlab

# 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:** ```bash # MATLAB (commercial) matlab -nodisplay -nosplash -r "run('script.m'); exit;" # GNU Octave (free, open-source) octave script.m ``` **Install GNU Octave:** ```bash # 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: ```matlab % 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](references/matrices-arrays.md). ### 2. Linear Algebra ```matlab % Eigenvalues and eigenvectors [V, D] = eig(A); % V: eigenvector...