Matrix transpose in MATLAB - Step-by-Step Execution

Concept Flow - Matrix transpose

Start with matrix A

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Read element A(i,j)

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Place element at position B(j,i)

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Repeat for all i,j

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Result: matrix B is transpose of A

The process reads each element of the original matrix and places it in the flipped position to create the transpose.

Execution Sample

MATLAB

A = [1 2 3; 4 5 6];
B = A';
disp(B);

This code creates a 2x3 matrix A, transposes it to a 3x2 matrix B, and displays B.

Execution Table

Step	Action	Element Read A(i,j)	Element Placed B(j,i)	Matrix B State
1	Read A(1,1)	1	B(1,1) = 1	[1 0; 0 0; 0 0]
2	Read A(1,2)	2	B(2,1) = 2	[1 0; 2 0; 0 0]
3	Read A(1,3)	3	B(3,1) = 3	[1 0; 2 0; 3 0]
4	Read A(2,1)	4	B(1,2) = 4	[1 4; 2 0; 3 0]
5	Read A(2,2)	5	B(2,2) = 5	[1 4; 2 5; 3 0]
6	Read A(2,3)	6	B(3,2) = 6	[1 4; 2 5; 3 6]
7	Transpose complete	-	-	Final B = [1 4; 2 5; 3 6]

💡 All elements of A read and placed in B with swapped indices.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	Final
A	[1 2 3; 4 5 6]	[1 2 3; 4 5 6]	[1 2 3; 4 5 6]	[1 2 3; 4 5 6]	[1 2 3; 4 5 6]	[1 2 3; 4 5 6]	[1 2 3; 4 5 6]	[1 2 3; 4 5 6]
B	empty 3x2	[1 0; 0 0; 0 0]	[1 0; 2 0; 0 0]	[1 0; 2 0; 3 0]	[1 4; 2 0; 3 0]	[1 4; 2 5; 3 0]	[1 4; 2 5; 3 6]	[1 4; 2 5; 3 6]

Key Moments - 3 Insights

Why does the size of matrix B change compared to A?

Because transpose swaps rows and columns, so a 2x3 matrix A becomes a 3x2 matrix B, as shown in the execution_table rows where indices are swapped.

Why is element A(1,2) placed at B(2,1) and not B(1,2)?

Transpose swaps the row and column indices, so element at row 1, column 2 in A goes to row 2, column 1 in B, as seen in step 2 of the execution_table.

Is the original matrix A changed after transpose?

No, A remains the same throughout, only B is created and filled, as shown in variable_tracker where A stays constant.

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what is the value placed in B and at which position?

A B(2,1) = 4

B B(1,2) = 4

C B(2,1) = 2

D B(1,1) = 4

💡 Hint

Check step 4 row in execution_table under 'Element Placed B(j,i)' column.

At which step does the last element of A get placed into B?

A Step 6

B Step 5

C Step 3

D Step 7

💡 Hint

Look at the last element read and placed in execution_table rows.

If matrix A was 3x2 instead of 2x3, what would be the size of B after transpose?

A 3x2

B 2x2

C 2x3

D 3x3

💡 Hint

Transpose swaps rows and columns, so check variable_tracker for size changes.

Concept Snapshot

Matrix transpose swaps rows and columns.
Syntax in MATLAB: B = A';
If A is m x n, B becomes n x m.
Each element A(i,j) moves to B(j,i).
Original matrix A stays unchanged.
Transpose is useful for flipping matrix orientation.

Full Transcript

Matrix transpose means flipping a matrix over its diagonal. We start with matrix A. For each element at row i and column j in A, we place it at row j and column i in matrix B. This swaps rows and columns. For example, a 2 by 3 matrix becomes a 3 by 2 matrix after transpose. The original matrix A does not change. The code A = [1 2 3; 4 5 6]; B = A'; disp(B); creates matrix A, transposes it to B, and displays B. Step by step, each element of A is read and placed in B at swapped indices. After all elements are processed, B is the transpose of A.