toqito.matrix_props.is_anti_hermitian

Checks if the matrix is an anti-Hermitian matrix.

Module Contents

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

Check if matrix is anti-Hermitian (a.k.a. skew-Hermitian) [@WikiAntiHerm].

An anti-Hermitian matrix is a complex square matrix that is equal to the negative of its own conjugate transpose.

Examples

Consider the following matrix:

[

A = begin{pmatrix}

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

end{pmatrix}

]

our function indicates that this is indeed an anti-Hermitian matrix as it holds that

[

A = -A^*.

]

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

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

print(is_anti_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 anti-Hermitian.

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

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

print(is_anti_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 anti-Hermitian, and False otherwise.

Return type:

bool