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Account for when factorizations and solvers are not well-defined #224

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Merged
merged 3 commits into from
Nov 4, 2021
Merged

Account for when factorizations and solvers are not well-defined #224

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8fe7f8c
Account for when factorizations may not be well-defined
lezcano Jul 14, 2021
ac312b7
Merge branch 'main' into 207
lezcano Jul 29, 2021
9251314
Merge branch 'main' into 207
kgryte Nov 4, 2021
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10 changes: 5 additions & 5 deletions spec/extensions/linear_algebra_functions.md
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Expand Up @@ -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`.

<!-- NOTE: once complex number support, each matrix must be Hermitian -->

Expand Down Expand Up @@ -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

Expand Down Expand Up @@ -465,13 +465,13 @@ 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**: _&lt;array&gt;_

- 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_

Expand Down Expand Up @@ -546,7 +546,7 @@ 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 = USVh` of a matrix (or a stack of matrices) `x`.
Computes a singular value decomposition `A = USVh` of a matrix (or a stack of matrices) `x`.

#### Parameters

Expand Down