linear_algebra.src.rayleigh_quotient
====================================

.. py:module:: linear_algebra.src.rayleigh_quotient

.. autoapi-nested-parse::

   https://en.wikipedia.org/wiki/Rayleigh_quotient



Functions
---------

.. autoapisummary::

   linear_algebra.src.rayleigh_quotient.is_hermitian
   linear_algebra.src.rayleigh_quotient.rayleigh_quotient
   linear_algebra.src.rayleigh_quotient.tests


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

.. py:function:: is_hermitian(matrix: numpy.ndarray) -> bool

   Checks if a matrix is Hermitian.
   >>> import numpy as np
   >>> A = np.array([
   ... [2,    2+1j, 4],
   ... [2-1j,  3,  1j],
   ... [4,    -1j,  1]])
   >>> is_hermitian(A)
   True
   >>> A = np.array([
   ... [2,    2+1j, 4+1j],
   ... [2-1j,  3,  1j],
   ... [4,    -1j,  1]])
   >>> is_hermitian(A)
   False


.. py:function:: rayleigh_quotient(a: numpy.ndarray, v: numpy.ndarray) -> Any

   Returns the Rayleigh quotient of a Hermitian matrix A and
   vector v.
   >>> import numpy as np
   >>> A = np.array([
   ... [1,  2, 4],
   ... [2,  3,  -1],
   ... [4, -1,  1]
   ... ])
   >>> v = np.array([
   ... [1],
   ... [2],
   ... [3]
   ... ])
   >>> rayleigh_quotient(A, v)
   array([[3.]])


.. py:function:: tests() -> None