toqito.matrix_props.is_rank_one
===============================

.. py:module:: toqito.matrix_props.is_rank_one

.. autoapi-nested-parse::

   Checks if a matrix has rank one.





Module Contents
---------------

.. py:function:: is_rank_one(mat, tol = 1e-08)

   Determine whether the given matrix has rank one [@WikiMatrixRank].

   The function evaluates the singular values (equivalently, eigenvalues for Hermitian matrices)
   and counts how many are greater than the provided tolerance.

   .. rubric:: Examples

   Consider the Bell state density matrix \(\rho = \ket{\Phi^+}\bra{\Phi^+}\). This matrix
   has rank one.

   ```python exec="1" source="above"
   from toqito.matrix_props import is_rank_one
   from toqito.states import bell

   rho = bell(0) @ bell(0).conj().T
   print(is_rank_one(rho))
   ```

   On the other hand, the maximally mixed state is not rank one.

   ```python exec="1" source="above"
   import numpy as np
   from toqito.matrix_props import is_rank_one

   maximally_mixed = np.eye(2) / 2
   print(is_rank_one(maximally_mixed))
   ```

   :param mat: Matrix to test.
   :param tol: Numerical tolerance used when distinguishing non-zero singular values.

   :returns: `True` if the matrix has rank at most one, `False` otherwise.