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is_hermitian() and is_skew_hermitian() over inexact rings #33053

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orlitzky opened this issue Dec 20, 2021 · 0 comments
Open

is_hermitian() and is_skew_hermitian() over inexact rings #33053

orlitzky opened this issue Dec 20, 2021 · 0 comments

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@orlitzky
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In #33031, the generic _is_hermitian() method for matrices was extended to support a tolerance, and sparse RDF/CDF matrices were made to use one by default. This works around numerical noise for those matrices, but the generic matrix implementation still uses a tolerance of zero, and does not allow the user to supply one. This leads to situations like,

sage: A = matrix(RR, [ [1, 1e-16],
....:                  [0, 1    ] ])
sage: A.is_hermitian()
False

where most people would argue that the matrix is Hermitian. Perhaps a small tolerance could be used by default for inexact rings, with the current tolerance of zero being retained for exact rings.

CC: @mwageringel

Component: linear algebra

Issue created by migration from https://trac.sagemath.org/ticket/33053

@orlitzky orlitzky added this to the sage-9.5 milestone Dec 20, 2021
@mkoeppe mkoeppe modified the milestones: sage-9.5, sage-9.6 Jan 10, 2022
@mkoeppe mkoeppe modified the milestones: sage-9.6, sage-9.7 Apr 7, 2022
@mkoeppe mkoeppe modified the milestones: sage-9.7, sage-9.8 Sep 19, 2022
@mkoeppe mkoeppe removed this from the sage-9.8 milestone Jan 29, 2023
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