toqito.matrix_props.is_orthonormal
==================================

.. py:module:: toqito.matrix_props.is_orthonormal

.. autoapi-nested-parse::

   Checks if the set of vectors are orthonormal.





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

.. py:function:: is_orthonormal(vectors)

   Check if the vectors are orthonormal.

   .. rubric:: Examples

   The following vectors are an example of an orthonormal set of
   vectors in \(\mathbb{R}^3\).

   \[
       \begin{pmatrix}
           1 \\ 0 \\ 1
       \end{pmatrix}, \quad
       \begin{pmatrix}
           1 \\ 1 \\ 0
       \end{pmatrix}, \quad \text{and} \quad
       \begin{pmatrix}
           0 \\ 0 \\ 1
       \end{pmatrix}
   \]

   To check these are a known set of orthonormal vectors:

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

   v_1 = np.array([1, 0, 0])
   v_2 = np.array([0, 1, 0])
   v_3 = np.array([0, 0, 1])

   v = np.array([v_1, v_2, v_3])

   print(is_orthonormal(v))
   ```

   :param vectors: A list of `np.ndarray` 1-by-n vectors.

   :returns: True if vectors are orthonormal; False otherwise.