The Cholesky decomposition of a Hermitian, but not positive-definite matrix

Ideas
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1

Possible bug in Wolfram|Alpha

The Cholesky decomposition only works for Hermitian and positive-definite matrices.

In Wolfram|Alpha:

  1. If one enters “Cholesky decomposition A” where A is a Hermitian and positive-definite matrix, WA responds with the correct decomposition.

  2. If one enters “Cholesky decomposition A” where A is not Hermitian, then WA correctly responds with “(matrix is not Hermitian)”.

  3. BUT if one enter “Cholesky decomposition A” where A is Hermitian, but not positive-definite, then WA doesn’t understand the query and either shows nothing or the definiton of the Cholesky decomposition. In my opinion, the correct thing to do would be to respond with “(matrix is not positive definite)” or something like that.

2

Thank you for your post.

I forwarded your report to “info@wolframalpha.com”.