Talk:Sylvester's criterion

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Hi, I was wondering if Sylvester's criterion applies to non-symmetric matrices as well. Can I conclude that a non-symmetric matrix is positive definite if the Sylvester's criterion is satisfied?


How does the Sylvester criterion work to show that a matrix is negative defined? I think it is if the principal minors are alternating between negative and positive (<, >, <, >, ...) then the matrix is negative-definite, but it would be nice to have it stated explicitly in the article. — Preceding unsigned comment added by 194.117.40.134 (talk) 15:26, 9 May 2014 (UTC)

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I point out that there might be a problem with sylvester's criterion as it is stated here regarding the leading principal minors. I found some contribution http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1100319 where it is stated that all principal minors have to be considered, not only the leading ones.

Could someone check this and correct it, if necessary?

--130.83.225.253 (talk) 12:24, 20 February 2015 (UTC)

It is true that for positive semi-definiteness it is needed to check all the principal minors of the matrix, but for positive-definiteness, only the leading principal minors need to be checked. Saung Tadashi (talk) 13:24, 20 February 2015 (UTC)