toqito.matrix_props.is_hermitian

Checks if the matrix is a Hermitian matrix.

Module Contents

toqito.matrix_props.is_hermitian.is_hermitian(mat, rtol=1e-05, atol=1e-08)

Check if matrix is Hermitian [@WikiHerm].

A Hermitian matrix is a complex square matrix that is equal to its own conjugate transpose.

Examples

Consider the following matrix:

[

A = begin{pmatrix}

2 & 2 +1j & 4 \ 2 - 1j & 3 & 1j \ 4 & -1j & 1

end{pmatrix}

]

our function indicates that this is indeed a Hermitian matrix as it holds that

[

A = A^*.

]

```python exec=”1” source=”above” import numpy as np from toqito.matrix_props import is_hermitian

mat = np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]])

print(is_hermitian(mat)) ```

Alternatively, the following example matrix (B) defined as

[

B = begin{pmatrix}

1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9

end{pmatrix}

]

is not Hermitian.

```python exec=”1” source=”above” import numpy as np from toqito.matrix_props import is_hermitian

mat = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

print(is_hermitian(mat)) ```

Parameters:

• mat (numpy.ndarray) – Matrix to check.

• rtol (float) – The relative tolerance parameter (default 1e-05).

• atol (float) – The absolute tolerance parameter (default 1e-08).

Returns:

Return True if matrix is Hermitian, and False otherwise.

Return type:

bool