# Documentation

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# `htranspose`

Hermitian transpose of a matrix

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## Syntax

```htranspose(`A`)
```

## Description

`htranspose(A)` returns the Hermitian transpose AH of the matrix A (the complex conjugate of the transpose of A). The Hermitian transpose of the m×n matrix A is the n×m matrix B with .

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

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

## 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

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 the transpose is the conjugate of the input:

`htranspose(A) + 2*htranspose(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`