`isposdef` inconsistent results, numerically unstable?

Specific Domains Numerics
32

I completely agree with @mohamed82008 in this topic. IMO we have two options to resolve the conflict.

  1. We restrict the domain of the function isposdef to symmetric real - and Hermitian matrices, that mean the method called for general real or complex matrices should throw MethodError, DomainError or ArgumentError.

  2. We extend the domain of isposdef to general matrices in the way Mathematica is doing it. That means, in the real and complex case we have to check A + A' for positive definiteness in the restricted sense.

I am in favour of option 2.

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