can one tell me when the block matrix M=[A B,C D] is positive definite such as:
1-the four block A,B,C and D are symmetric diagonal positive definite matrices
2-M is asymmetric, so C is not the transpose of B, and we can not apply schur formula
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Why can't we apply the Schur complement? – Wintermute Mar 28 '13 at 13:53
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because C is not the transpose of B – fidel Mar 28 '13 at 14:03
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You are looking at a particular case of the Schur complement. A sufficient condition that $M$ be positive definite is that the Schur complement $A-BD^{-1}C$ be positive definite. – Wintermute Mar 28 '13 at 14:15
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but for my knowldege, the schure complement is applied when C is the transpose of B – fidel Mar 28 '13 at 14:22
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You can use the Schur complement in more general situations. See here, it talks about both. http://en.wikipedia.org/wiki/Schur_complement – Wintermute Mar 28 '13 at 18:00
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you can not, go to the site web you gave me and see that when we use the shure complement to talk about positive defintnesse, C should be the transpose of B – fidel Apr 01 '13 at 13:41