.. _routines.linalg:

.. module:: mxnet.np.linalg

Linear algebra (:mod:`numpy.linalg`)
************************************

The NumPy linear algebra functions rely on BLAS and LAPACK to provide efficient
low level implementations of standard linear algebra algorithms. Those
libraries may be provided by NumPy itself using C versions of a subset of their
reference implementations but, when possible, highly optimized libraries that
take advantage of specialized processor functionality are preferred. Examples
of such libraries are OpenBLAS_, MKL (TM), and ATLAS. Because those libraries
are multithreaded and processor dependent, environmental variables and external
packages such as threadpoolctl_ may be needed to control the number of threads
or specify the processor architecture.

.. _OpenBLAS: https://www.openblas.net/
.. _threadpoolctl: https://github.com/joblib/threadpoolctl

.. currentmodule:: mxnet.np

Matrix and vector products
--------------------------
.. autosummary::
   :toctree: generated/

   dot
   vdot
   inner
   outer
   tensordot
   einsum

::

   linalg.multi_dot
   matmul
   einsum_path
   linalg.matrix_power
   kron

Decompositions
--------------
.. autosummary::
   :toctree: generated/

   linalg.svd

::

   linalg.cholesky
   linalg.qr

Matrix eigenvalues
------------------
.. autosummary::
   :toctree: generated/


::

   linalg.eig
   linalg.eigh
   linalg.eigvals
   linalg.eigvalsh

Norms and other numbers
-----------------------
.. autosummary::
   :toctree: generated/

   linalg.norm
   trace

::

   linalg.cond
   linalg.det
   linalg.matrix_rank
   linalg.slogdet

Solving equations and inverting matrices
----------------------------------------
.. autosummary::
   :toctree: generated/


::

   linalg.solve
   linalg.tensorsolve
   linalg.lstsq
   linalg.inv
   linalg.pinv
   linalg.tensorinv

Exceptions
----------
.. autosummary::
   :toctree: generated/


::

   linalg.LinAlgError