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[Octave-bug-tracker] [bug #51270] isdefinite should return 0 for zero ma
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From: |
Marco Caliari |
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Subject: |
[Octave-bug-tracker] [bug #51270] isdefinite should return 0 for zero matrices |
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Date: |
Thu, 22 Jun 2017 03:29:33 -0400 (EDT) |
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User-agent: |
Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:54.0) Gecko/20100101 Firefox/54.0 |
Follow-up Comment #6, bug #51270 (project octave):
There is no way to determine positive-definiteness cheaper than Choleski, as
far as I know. Then, for any default tolerance tol
[1, 0; 0, -tol / 2]
will be detected as positive semi-definite. I am in favour of isdefinite
returning either true (positive definite) or false. In the documentation it
would possible to write that if isdefinite(A) is false but isdefinite(A+tol)
is true for tol sufficiently small, than A is quite surely semi-definite. And,
if one wants to be sure (up to machine precision), the eigenvalues have to be
computed.
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