matlab

1# MATLAB/Octave Scientific Computing
2 
3MATLAB is a numerical computing environment optimized for matrix operations and scientific computing. GNU Octave is a free, open-source alternative with high MATLAB compatibility.
4 
5## Quick Start
6 
7**Running MATLAB scripts:**
8```bash
9# MATLAB (commercial)
10matlab -nodisplay -nosplash -r "run('script.m'); exit;"
11 
12# GNU Octave (free, open-source)
13octave script.m
14```
15 
16**Install GNU Octave:**
17```bash
18# macOS
19brew install octave
20 
21# Ubuntu/Debian
22sudo apt install octave
23 
24# Windows - download from https://octave.org/download
25```
26 
27## Core Capabilities
28 
29### 1. Matrix Operations
30 
31MATLAB operates fundamentally on matrices and arrays:
32 
33```matlab
34% Create matrices
35A = [1 2 3; 4 5 6; 7 8 9];  % 3x3 matrix
36v = 1:10;                     % Row vector 1 to 10
37v = linspace(0, 1, 100);      % 100 points from 0 to 1
38 
39% Special matrices
40I = eye(3);          % Identity matrix
41Z = zeros(3, 4);     % 3x4 zero matrix
42O = ones(2, 3);      % 2x3 ones matrix
43R = rand(3, 3);      % Random uniform
44N = randn(3, 3);     % Random normal
45 
46% Matrix operations
47B = A';              % Transpose
48C = A * B;           % Matrix multiplication
49D = A .* B;          % Element-wise multiplication
50E = A \ b;           % Solve linear system Ax = b
51F = inv(A);          % Matrix inverse
52```
53 
54For complete matrix operations, see [references/matrices-arrays.md](references/matrices-arrays.md).
55 
56### 2. Linear Algebra
57 
58```matlab
59% Eigenvalues and eigenvectors
60…