polymerist.maths.linearalg.decomposition
========================================

.. py:module:: polymerist.maths.linearalg.decomposition

.. autoapi-nested-parse::

   Tools for matrix decomposition



Functions
---------

.. autoapisummary::

   polymerist.maths.linearalg.decomposition.diagonalize
   polymerist.maths.linearalg.decomposition.inv_left
   polymerist.maths.linearalg.decomposition.inv_right


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

.. py:function:: diagonalize(matrix: numpy.ndarray) -> tuple[numpy.ndarray]

   Diagonalize a matrix into it's eigenbasis. Return rotation and diagonal matrices P, D, and P^-1


.. py:function:: inv_left(matrix: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.M, polymerist.genutils.typetools.numpytypes.N], polymerist.genutils.typetools.numpytypes.DType]) -> numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.M], polymerist.genutils.typetools.numpytypes.DType]

   Return the left-inverse of an arbitrary (not necessarily square) matrix


.. py:function:: inv_right(matrix: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.M, polymerist.genutils.typetools.numpytypes.N], polymerist.genutils.typetools.numpytypes.DType]) -> numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.M], polymerist.genutils.typetools.numpytypes.DType]

   Return the right-inverse of an arbitrary (not necessarily square) matrix