toqito.matrix_props.is_idempotent

Checks if the matrix is an idempotent matrix.

Module Contents

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

Check if matrix is the idempotent matrix [@WikiIdemPot].

An idempotent matrix is a square matrix, which, when multiplied by itself, yields itself. That is, the matrix (A) is idempotent if and only if (A^2 = A).

Examples

The following is an example of a (2 x 2) idempotent matrix:

[

A = begin{pmatrix}

3 & -6 \ 1 & -2

end{pmatrix}

]

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

mat = np.array([[3, -6], [1, -2]])

print(is_idempotent(mat)) ```

Alternatively, the following matrix

[

B = begin{pmatrix}

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

end{pmatrix}

]

is not idempotent.

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

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

print(is_idempotent(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 the idempotent matrix, and False otherwise.

Return type:

bool