qml.math.binary_matrix_rank

binary_matrix_rank(binary_matrix)

Find the rank of a matrix over \(\mathbb{Z}_2\).

Parameters:

binary_matrix (np.ndarray) – Matrix of binary entries.

Returns:

Rank of binary_matrix over the finite field \(\mathbb{Z}_2\).

Return type:

int

Note that the ranks of a matrix over \(\mathbb{Z}_2\) and over \(\mathbb{Z}\) (or \(\mathbb{R}\)) may differ.

This function does not modify the input.

Warning

This function is currently not compatible with JAX.

Example

Consider the following binary matrix of shape (4, 4):

>>> binary_matrix = np.array([
...     [0, 1, 1, 0],
...     [0, 1, 0, 1],
...     [1, 0, 1, 1],
...     [1, 0, 0, 0],
... ])
>>> print(binary_matrix.shape)
(4, 4)

We may compute its rank over \(\mathbb{Z}_2\) and find that it does not have full rank:

>>> print(qml.math.binary_matrix_rank(binary_matrix))
3

Note that it would have full rank over the real numbers \(\mathbb{R}\):

>>> print(qml.math.linalg.matrix_rank(binary_matrix))
4

code/api/pennylane.math.binary_matrix_rank

 

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