toqito.matrix_props.is_symmetric

Checks if the matrix is a symmetric matrix.

Module Contents

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

Determine if a matrix is symmetric [@WikiSymMat].

The following 3x3 matrix is an example of a symmetric matrix:

[

begin{pmatrix}

1 & 7 & 3 \ 7 & 4 & -5 \ 3 &-5 & 6

end{pmatrix}

]

Examples

Consider the following matrix

[

A = begin{pmatrix}

1 & 7 & 3 \ 7 & 4 & -5 \ 3 & -5 & 6

end{pmatrix}

]

our function indicates that this is indeed a symmetric matrix.

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

A = np.array([[1, 7, 3], [7, 4, -5], [3, -5, 6]])

print(is_symmetric(A)) ```

Alternatively, the following example matrix (B) defined as

[

B = begin{pmatrix}

1 & 2 \ 4 & 5

end{pmatrix}

]

is not symmetric.

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

B = np.array([[1, 2], [3, 4]])

print(is_symmetric(B)) ```

Parameters:

• mat (numpy.ndarray) – The matrix to check.

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

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

Returns:

Returns True if the matrix is symmetric and False otherwise.

Return type:

bool