toqito.matrices.comparison

Computes comparison matrix.

Module Contents

toqito.matrices.comparison.comparison(mat)

Compute comparison matrix of a given square matrix.

This function computes the comparison matrix (M(A)) for a square matrix (A) as defined in [@WikiComparisonMatrix]. For each entry, the diagonal entries are given by the absolute value of the original diagonal entries of (A), while the off-diagonal entries are given by minus the absolute value of the corresponding entries. In other words,

[

m_{ij} = begin{cases} |a_{ij}|, & text{if } i = j, \ -|a_{ij}|, & text{if } i neq j. end{cases}

]

Examples

```python exec=”1” source=”above” import numpy as np from toqito.matrices import comparison A = np.array([[2, -1],

[3, 4]])

print(comparison(A)) ```

Raises:

ValueError – If the input matrix is not square.

Parameters:

mat (numpy.ndarray) – The input square matrix.

Returns:

The comparison matrix of the input matrix.

Return type:

numpy.ndarray