Creating, Concatenating, and Expanding Matrices - MATLAB & Simulink

In MATLAB and Simulink, working with matrices is a fundamental task. Here's a guide on creating, concatenating, and expanding matrices:

Creating Matrices

1. Directly Creating Matrices:

   • You can create matrices directly by specifying the elements in square brackets [].

   matlab

   % Create a 2x3 matrix
   A = [1, 2, 3; 4, 5, 6];
   

2. Using Functions:

   • Use functions like zeros, ones, eye, and rand to create matrices with specific properties.

   matlab

   % Create a 3x3 matrix of zeros
   Z = zeros(3);
   
   % Create a 3x3 matrix of ones
   O = ones(3);
   
   % Create a 3x3 identity matrix
   I = eye(3);
   
   % Create a 3x3 matrix with random elements
   R = rand(3);
   

Concatenating Matrices

1. Horizontal Concatenation:

   • Concatenate matrices side-by-side using square brackets [].

   matlab

   A = [1, 2, 3];
   B = [4, 5, 6];
   C = [A, B]; % Result: [1, 2, 3, 4, 5, 6]
   

2. Vertical Concatenation:

   • Concatenate matrices top-to-bottom using semicolons ;.

   matlab

   A = [1, 2, 3];
   B = [4, 5, 6];
   C = [A; B]; % Result: [1, 2, 3; 4, 5, 6]
   

Expanding Matrices

1. Expanding by Assignment:

   • Expand a matrix by directly assigning values to elements outside the current size.

   matlab

   A = [1, 2, 3];
   A(2, 4) = 10; % Expands A to 2x4: [1, 2, 3, 0; 0, 0, 0, 10]
   

2. Using Functions:

   • Use the padarray function from the Image Processing Toolbox to pad matrices.

   matlab

   A = [1, 2, 3];
   B = padarray(A, [1, 1], 0, 'post'); % Pads with zeros at the end
   

Example of Creating, Concatenating, and Expanding Matrices

% Create matrices
A = [1, 2; 3, 4];
B = [5, 6; 7, 8];

% Horizontal concatenation
C_hor = [A, B]; % Result: [1, 2, 5, 6; 3, 4, 7, 8]

% Vertical concatenation
C_ver = [A; B]; % Result: [1, 2; 3, 4; 5, 6; 7, 8]

% Expanding matrices
A(3, 3) = 9; % Expands A to 3x3: [1, 2, 0; 3, 4, 0; 0, 0, 9]

% Display results
disp('Horizontal Concatenation:');
disp(C_hor);
disp('Vertical Concatenation:');
disp(C_ver);
disp('Expanded Matrix:');
disp(A);

These techniques will help you efficiently create, concatenate, and expand matrices in MATLAB and Simulink