Linear algebra (numpy.linalg
)¶
Matrix and vector products¶
Decompositions¶
Matrix eigenvalues¶
Norms and other numbers¶
Solving equations and inverting matrices¶
Exceptions¶
Linear algebra on several matrices at once¶
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.