# Documentation

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# `transpose`

Transpose of a matrix

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

For the `transpose` function in MATLAB®, see `transpose`.

## Syntax

```transpose(`A`)
```

## Description

`transpose(A)` returns the transpose At of the matrix A. The transpose of the m×n matrix A is the n×m matrix B such that Bi, j = Aj, i.

If the input is a matrix of category `Cat::Matrix`, then internally `linalg::transpose` computes the result. For `arrays` and `hfarrays`, `transpose` uses other routines.

If the argument does not evaluate to a matrix of one of these types, the transpose is the input itself.

## Examples

### Example 1

Compute the transpose of the following real matrix. For real matrices, the Hermitian transpose coincides with the transpose:

`A := matrix([[1, 2], [3, PI]])`

`transpose(A) = htranspose(A)`

In general, this does not hold for complex matrices:

`A := matrix([[1, I, 3 + I], [PI*I, 4, 5]])`

`transpose(A) <> htranspose(A)`

`delete A:`

### Example 2

If the input does not evaluate to a matrix, then the transpose is the input itself:

`transpose(A) + 2*transpose(B)`

## Parameters

 `A` An object of the category `Cat::Matrix`, a two-dimensional `array`, or a two-dimensional `hfarray`.

## Return Values

Object of the same domain type as `A`.

`A`