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.. _routines.linalg:
Linear algebra (:mod:`numpy.linalg`)
************************************
.. currentmodule:: numpy
Matrix and vector products
--------------------------
.. autosummary::
:toctree: generated/
dot
linalg.multi_dot
vdot
inner
outer
matmul
tensordot
einsum
einsum_path
linalg.matrix_power
kron
Decompositions
--------------
.. autosummary::
:toctree: generated/
linalg.cholesky
linalg.qr
linalg.svd
Matrix eigenvalues
------------------
.. autosummary::
:toctree: generated/
linalg.eig
linalg.eigh
linalg.eigvals
linalg.eigvalsh
Norms and other numbers
-----------------------
.. autosummary::
:toctree: generated/
linalg.norm
linalg.cond
linalg.det
linalg.matrix_rank
linalg.slogdet
trace
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
.. _routines.linalg-broadcasting:
Linear algebra on several matrices at once
------------------------------------------
.. versionadded:: 1.8.0
Several of the linear algebra routines listed above are able to
compute results for several matrices at once, if they are stacked into
the same array.
This is indicated in the documentation via input parameter
specifications such as ``a : (..., M, M) array_like``. This means that
if for instance given an input array ``a.shape == (N, M, M)``, it is
interpreted as a "stack" of N matrices, each of size M-by-M. Similar
specification applies to return values, for instance the determinant
has ``det : (...)`` and will in this case return an array of shape
``det(a).shape == (N,)``. This generalizes to linear algebra
operations on higher-dimensional arrays: the last 1 or 2 dimensions of
a multidimensional array are interpreted as vectors or matrices, as
appropriate for each operation.
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