toqito.matrix_props.is_identity

Checks if the matrix is an identity matrix.

Module Contents

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

Check if matrix is the identity matrix [@WikiIden].

For dimension (n), the (n times n) identity matrix is defined as

[

I_n = begin{pmatrix}

1 & 0 & 0 & ldots & 0 \ 0 & 1 & 0 & ldots & 0 \ 0 & 0 & 1 & ldots & 0 \ vdots & vdots & vdots & ddots & vdots \ 0 & 0 & 0 & ldots & 1

end{pmatrix}.

]

Examples

Consider the following matrix:

[

A = begin{pmatrix}

1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1

end{pmatrix}

]

our function indicates that this is indeed the identity matrix of dimension 3.

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

mat = np.eye(3)

print(is_identity(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 an identity matrix.

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

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

print(is_identity(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 identity matrix, and False otherwise.

Return type:

bool