From 8fe7f8cda63f73ffc55a58b1ddf83b07f790888f Mon Sep 17 00:00:00 2001 From: lezcano Date: Wed, 14 Jul 2021 10:45:03 +0100 Subject: [PATCH] Account for when factorizations may not be well-defined --- spec/extensions/linear_algebra_functions.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/spec/extensions/linear_algebra_functions.md b/spec/extensions/linear_algebra_functions.md index 423e17b85..11a281cf8 100644 --- a/spec/extensions/linear_algebra_functions.md +++ b/spec/extensions/linear_algebra_functions.md @@ -182,7 +182,7 @@ _TODO: this requires complex number support to be added to the specification._ (function-linalg-eigh)= ### linalg.eigh(x, /, *, upper=False) -Returns the eigenvalues and eigenvectors of a symmetric matrix (or a stack of symmetric matrices) `x`. +Returns an eigendecomposition of a symmetric matrix (or a stack of symmetric matrices) `x`. @@ -270,7 +270,7 @@ Computes the multiplicative inverse of a square matrix (or a stack of square mat (function-linalg-lstsq)= ### linalg.lstsq(x1, x2, /, *, rtol=None) -Returns the least-squares solution to a linear matrix equation `Ax = b`. +Returns the minimum-norm least-squares solution to a linear matrix equation `Ax = b`. #### Parameters @@ -470,13 +470,13 @@ Computes the (Moore-Penrose) pseudo-inverse of a matrix (or a stack of square ma (function-linalg-qr)= ### linalg.qr(x, /, *, mode='reduced') -Computes the qr factorization of a matrix (or a stack of matrices), where `q` is an orthonormal matrix (or a stack of matrices) and `r` is an upper-triangular matrix (or a stack of matrices). +Computes the qr factorization of a full column rank matrix (or a stack of matrices), where `q` is an orthonormal matrix (or a stack of matrices) and `r` is an upper-triangular matrix (or a stack of matrices). #### Parameters - **x**: _<array>_ - - input array having shape `(..., M, N)` and whose innermost two dimensions form `MxN` matrices. Should have a floating-point data type. + - input array having shape `(..., M, N)` and whose innermost two dimensions form `MxN` matrices of rank equal to `N`. Should have a floating-point data type. - **mode**: _str_ @@ -551,7 +551,7 @@ Returns the solution to the system of linear equations represented by the well-d (function-linalg-svd)= ### linalg.svd(x, /, *, full_matrices=True) -Computes the singular value decomposition `A = USV` of a matrix (or a stack of matrices) `x`. +Computes a singular value decomposition `A = USV` of a matrix (or a stack of matrices) `x`. #### Parameters @@ -648,4 +648,4 @@ Alias for {ref}`function-transpose`. (function-linalg-vecdot)= ### linalg.vecdot(x1, x2, /, *, axis=None) -Alias for {ref}`function-vecdot`. \ No newline at end of file +Alias for {ref}`function-vecdot`.