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# transpose

Transpose of a matrix

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## 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 with Bi, j = Aj, i.

If the input is a matrix of category Cat::Matrix, then linalg::transpose is called to compute the result. In contrast to the linalg routines, the function transpose also operates on arrays and hfarrays.

If the argument does not evaluate to a matrix of one of the types mentioned above, symbolic call transpose(A) is returned.

## Examples

### Example 1

The following matrix is real. Thus, the Hermitian transpose coincides with the transpose:

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

`transpose(A) = htranspose(A)`

In general, this does not hold for complex matrices:

`A := hfarray(1..2, 1..3, [[1, I, 3 + I], [PI*I, 4, 5]])`

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

`delete A:`

### Example 2

We compute the product AHA of a matrix given by a hardware float array. This data type allows matrix multiplication using the operator *:

`A := hfarray(1..2, 1..3, [[1, I, 3], [PI*I, 4, 5 + I]])`

`AH:= htranspose(A)`

The product AHA is Hermitian:

`AH*A = htranspose(AH*A)`

`delete A, AH:`

### Example 3

If the input does not evaluate to a matrix, then symbolic calls are returned:

```delete A, B:
transpose(A) + 2*htranspose(B)```

## Parameters

 A A matrix: either a 2-dimensional array, a 2-dimensional hfarray, or an object of the category Cat::Matrix

## Return Values

Matrix of the same domain type as A.

A

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