Matrix concatenation in MATLAB - Step-by-Step Execution

Concept Flow - Matrix concatenation

Define matrices A and B

↓

Choose concatenation direction

↓

Horizontal concat

↓

Combine side-by-side

↓

Resulting matrix C

↓

Use C

Start with two matrices, decide to join them side-by-side (horizontal) or top-to-bottom (vertical), then combine to get a new matrix.

Execution Sample

MATLAB

A = [1 2; 3 4];
B = [5 6; 7 8];
C = [A B];
D = [A; B];

Create two 2x2 matrices A and B, then concatenate horizontally into C and vertically into D.

Execution Table

Step	Operation	Matrices Involved	Resulting Matrix	Size
1	Define A	None	[1 2; 3 4]	2x2
2	Define B	None	[5 6; 7 8]	2x2
3	Horizontal concat C = [A B]	A, B	[1 2 5 6; 3 4 7 8]	2x4
4	Vertical concat D = [A; B]	A, B	[1 2; 3 4; 5 6; 7 8]	4x2
5	End	None	No more operations	-

💡 All concatenations done; matrices combined horizontally and vertically.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	Final
A	undefined	[1 2; 3 4]	[1 2; 3 4]	[1 2; 3 4]	[1 2; 3 4]	[1 2; 3 4]
B	undefined	undefined	[5 6; 7 8]	[5 6; 7 8]	[5 6; 7 8]	[5 6; 7 8]
C	undefined	undefined	undefined	[1 2 5 6; 3 4 7 8]	[1 2 5 6; 3 4 7 8]	[1 2 5 6; 3 4 7 8]
D	undefined	undefined	undefined	undefined	[1 2; 3 4; 5 6; 7 8]	[1 2; 3 4; 5 6; 7 8]

Key Moments - 2 Insights

Why does horizontal concatenation require the same number of rows in A and B?

Because when joining side-by-side, each row from A must line up with a row from B. If rows differ, MATLAB cannot align them, causing an error. See step 3 in execution_table where both A and B have 2 rows.

Why must vertical concatenation have the same number of columns?

When stacking matrices top-to-bottom, columns must match so each column aligns vertically. Step 4 shows A and B both have 2 columns, allowing vertical concatenation.

Visual Quiz - 3 Questions

Look at the execution_table at step 3. What is the size of matrix C after horizontal concatenation?

A 4x2

B 2x4

C 2x2

D 4x4

💡 Hint

Check the 'Size' column in execution_table row for step 3.

At which step does matrix D get its value?

A Step 2

B Step 3

C Step 4

D Step 5

💡 Hint

Look for vertical concatenation operation in execution_table.

If matrix B had 3 rows instead of 2, what would happen at step 3?

A Error due to row mismatch

B Horizontal concatenation would succeed with larger C

C Vertical concatenation would fail instead

D No change, concatenation works

💡 Hint

Recall key_moments about row matching for horizontal concatenation.

Concept Snapshot

Matrix concatenation in MATLAB:
- Use [A B] for horizontal (side-by-side) concatenation.
- Use [A; B] for vertical (top-to-bottom) concatenation.
- Horizontal concat requires same number of rows.
- Vertical concat requires same number of columns.
- Resulting matrix size depends on concat direction.

Full Transcript

This visual trace shows how MATLAB concatenates matrices. First, matrices A and B are defined as 2x2. Then, horizontal concatenation [A B] joins them side-by-side, resulting in a 2x4 matrix C. Vertical concatenation [A; B] stacks them top-to-bottom, creating a 4x2 matrix D. Key rules are that horizontal concatenation needs matching rows, and vertical concatenation needs matching columns. The variable tracker shows how A, B, C, and D change step-by-step. The quiz checks understanding of sizes and errors if dimensions don't match.