# Documentation

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# `linalg`::`isHermitian`

Checks whether a matrix is Hermitian

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## Syntax

```linalg::isHermitian(`A`)
```

## Description

`linalg::isHermitian(A)` determines whether the matrix A is Hermitian, i.e., whether , where denotes the conjugate matrix.

If the component ring of the matrix `A` does not provide the method `"conjugate"`, then `A` is tested for symmetry, i.e., `linalg::isHermitian` returns `TRUE` if and only if `A` satisfies the equation A = At.

## Examples

### Example 1

Here is an example of a Hermitian matrix:

`A := Dom::Matrix(Dom::Complex)([[1, I], [-I, 1]])`

`linalg::isHermitian(A)`

The following matrix is not Hermitian:

`B := Dom::Matrix(Dom::Complex)([[1, -I], [-I, 1]])`

`linalg::isHermitian(B)`

The reason is the following:

`linalg::transpose(conjugate(B)) <> B`

### Example 2

Here is an example of a symmetric matrix over the integers:

`C := Dom::Matrix(Dom::Integer)([[1, 2], [2, -1]])`

`linalg::isHermitian(C)`

## Parameters

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

## Return Values

Either `TRUE` or `FALSE`.