How to Concatenate Matrices in MATLAB: Syntax and Examples

In MATLAB, you concatenate matrices using square brackets []. Use [A, B] to join matrices horizontally (side by side) and [A; B] to join them vertically (one on top of the other).

Syntax

To concatenate matrices in MATLAB, use square brackets []. Horizontal concatenation places matrices side by side, separated by commas or spaces. Vertical concatenation stacks matrices on top of each other, separated by semicolons.

• Horizontal: [A, B] or [A B]
• Vertical: [A; B]

Both matrices must have compatible sizes: for horizontal concatenation, they must have the same number of rows; for vertical, the same number of columns.

matlab

[A, B]  % Horizontal concatenation
[A; B]  % Vertical concatenation

Example

This example shows how to concatenate two matrices horizontally and vertically. It demonstrates the syntax and the resulting matrices.

matlab

A = [1 2 3; 4 5 6];
B = [7 8 9; 10 11 12];

% Horizontal concatenation
H = [A, B];

% Vertical concatenation
V = [A; B];

H
V

Output

H =
     1     2     3     7     8     9
     4     5     6    10    11    12

V =
     1     2     3
     4     5     6
     7     8     9
    10    11    12

Common Pitfalls

Common mistakes when concatenating matrices include:

• Trying to concatenate matrices with incompatible sizes (different row counts for horizontal, or different column counts for vertical).
• Using commas instead of semicolons for vertical concatenation or vice versa.
• Confusing horizontal and vertical concatenation syntax.

Always check matrix dimensions before concatenation.

matlab

% Wrong: different row counts for horizontal concatenation
A = [1 2; 3 4];
B = [5 6 7];
% This will cause an error:
% C = [A, B];

% Correct approach: adjust sizes or use vertical concatenation if columns match
B = [5 6];
C = [A; B];  % Works if columns match

Quick Reference

Summary of matrix concatenation in MATLAB:

Operation	Syntax	Requirement
Horizontal Concatenation	[A, B] or [A B]	Same number of rows
Vertical Concatenation	[A; B]	Same number of columns

Key Takeaways

Use square brackets [] to concatenate matrices in MATLAB.

Use commas or spaces for horizontal concatenation; use semicolons for vertical concatenation.

Ensure matrices have compatible dimensions before concatenating.

Horizontal concatenation requires matching row counts; vertical requires matching column counts.

Check matrix sizes to avoid dimension mismatch errors.