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# Matlab Transpose

Transpose is used in mathematics to interchange the rows and columns of the input matrix. So, if we have a 2 x 3 matrix as our input, the transpose function will give us a 3 x 2 matrix as the output. In Matlab, we use the ‘transpose function’ to compute the transpose of a matrix or a vector. For a vector with ‘n’ elements, the transpose function gives a ‘n x 1’ matrix as output (‘n’ rows and 1 column).

## Syntax of transpose function:

`T = transpose (M)`

`T = M.’`

## Explanation:

• T = transpose (M) is used to compute the transpose of the input matrix ‘M’, i.e., it will interchange the rows and columns of the matrix ‘M’.
• T = M.’ is another way of computing the transpose. It will give the same output as the above syntax.

## Examples of Matlab Transpose

Given below are the examples of Matlab Transpose:

## Example #1

In this example, we will use the transpose function to compute the transpose of a 2 x 2 real matrix.

Below are the steps to be followed:

• Initialize the input matrix.
• Pass this input matrix as an argument to the transpose function.

## Code:

M = [6 -5; 1 6] [Initializing the 2 x 2 input matrix]

T = transpose (M)
[Using the transpose function to compute the transpose of the input matrix]

## Output:

Before transpose:

After transpose:

As we can see in the output, the transpose function has interchanged the rows and columns of our input matrix.

## Example #2

In this example, we will use the transpose function to compute the transpose of a 3 x 3 real matrix.

Below are the steps to be followed:

• Initialize the input matrix.
• Pass this input matrix as an argument to the transpose function.

## Code:

M = [2 -1 4; 1 16 2; 0 -4 3] [Initializing the 3 x 3 input matrix]

T = transpose (M)
[Using the transpose function to compute the transpose of the input matrix]

• Input:

## Output:

Before transpose:

After transpose:

As we can see in the output, the transpose function has interchanged the rows and columns of our input matrix.

In the above 2 examples, our input matrix was of real elements.

Next, let us take an example where our input matrix will have complex elements as well.

## Example #3

In this example, we will use the transpose function to compute the transpose of a 3 x 3 complex matrix.

Below are the steps to be followed:

• Initialize the input matrix with complex elements.
• Pass this input matrix as an argument to the transpose function.

## Code:

M = [2+3i 1-4i 1; 1+3i 0 3-2i; 0 3 2] [Initializing the 3 x 3 input matrix with complex elements]

T = transpose (M)
[Using the transpose function to compute the transpose of the input matrix]

## Output:

Before transpose:

After transpose:

As we can see in the output, the transpose function has interchanged the rows and columns of our input complex matrix.

In the above 3 examples, we have used a square matrix as our input.

Next, we will use a non-square matrix as input to the transpose function.

## Example #4

In this example, we will use the transpose function to compute the transpose of a 2 x 3 real matrix.

Below are the steps to be followed:

• Initialize the input matrix.
• Pass this input matrix as an argument to the transpose function.

## Code:

M = [1 6 4; 1 4 -2] [Initializing the 2 x 3 input matrix]

T = transpose (M)
[Using the transpose function to compute the transpose of the input matrix]

## Output:

Before transpose:

After transpose:

As we can see in the output, the transpose function has interchanged the rows and columns of our non-square input matrix.

In the above 4 examples, we have used a matrix as our input to the transpose function.

Next, we will use the transpose function to compute the transpose of a vector input.

## Example #5

In this example, we will use the transpose function to compute the transpose of a vector with 5 elements.

Below are the steps to be followed:

• Initialize the input vector with 5 elements.
• Pass this input vector as an argument to the transpose function.

## Code:

M = [8 -11 4 5 7] [Initializing the input vector with 5 elements]

T = transpose (M)
[Using the transpose function to compute the transpose of the input vector] Please note that since our input has 5 columns and 1 row, our output will have 5 rows and 1 column.

## Output:

Before transpose:

After transpose:

As we can see in the output, the transpose function has interchanged our input vector rows and columns.