toqito.matrices.cyclic_permutation_matrix

Generates a cyclic permutation matrix.

Module Contents

toqito.matrices.cyclic_permutation_matrix.cyclic_permutation_matrix(n, k=1)[source]

Create the cyclic permutation matrix for a given dimension n [@WikiCyclicPermutation].

This function creates a cyclic permutation matrix of 0’s and 1’s which is a special type of square matrix that represents a cyclic permutation of its rows. The function allows fixed points and successive applications.

Examples

Generate fixed point.

```python exec=”1” source=”above” from toqito.matrices import cyclic_permutation_matrix

print(cyclic_permutation_matrix(n=4)) ```

Generate successive application.

```python exec=”1” source=”above” from toqito.matrices import cyclic_permutation_matrix

print(cyclic_permutation_matrix(n=4, k=3)) ```

Parameters:

  • n (int) – int The number of rows and columns in the cyclic permutation matrix.

  • k (int) – int The power to which the elements are raised, representing successive applications.

Returns:

A NumPy array representing a cyclic permutation matrix of dimension n x n. Each row of the matrix is shifted one position to the right in a cyclic manner, creating a circular permutation pattern. If k is specified, the function raises the matrix to the power of k, representing successive applications of the cyclic permutation.

Return type:

numpy.ndarray