# Documentation

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# `linalg`::`transpose`

Transpose of a matrix

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## Syntax

```linalg::transpose(`A`)
```

## Description

`linalg::transpose(A)` returns the transpose At of the matrix A.

`linalg::transpose` is an interface function for the method `"transpose"` of the matrix domain of `A`, i.e., instead of `linalg::transpose(A)` one may call `A::dom::transpose(A)` directly.

## Examples

### Example 1

We define a 3×4 matrix:

`A := matrix([[1, 2, 3, 4], [-1, 0, 1, 0], [3, 5, 6, 9]])`

Then the transpose of `A` is the 4 ×3 matrix:

`linalg::transpose(A)`

## Parameters

 `A` A matrix of a domain of category `Cat::Matrix`

## Return Values

Matrix of the same domain type as `A`.

## Algorithms

Let A = (ai, j)1 ≤ im, 1 ≤ jn be an m×n matrix. Then the transpose of A is the n×m matrix:

.