Postive-Definiteness

M.A · **Joined:** Thu, 26 Jul 2007 19:08:57 UTC **Posts:** 48

Here is a simple and a short question:
Suppose we have the following positive definite matrix consisting of block matrices given as:
$\left[ {\begin{array}{*{20}c} {A_1 } & {A_4 } & {A_6 } \\ {A_4^T } & {A_2 } & {A_5 } \\ {A_6^T } & {A_5^T } & {A_3 } \\ \end{array}} \right]>0$
Then, Is it true that A_1>0, A_2>0,A_3>0

?

Thanks

outermeasure · **Posted:** Sun, 20 Jun 2010 03:02:23 UTC

M.A wrote:

Here is a simple and a short question:
Suppose we have the following positive definite matrix consisting of block matrices given as:
$\left[ {\begin{array}{*{20}c} {A_1 } & {A_4 } & {A_6 } \\ {A_4^T } & {A_2 } & {A_5 } \\ {A_6^T } & {A_5^T } & {A_3 } \\ \end{array}} \right]>0$
Then, Is it true that A_1>0, A_2>0,A_3>0

?

Thanks

Yes. Restriction of a quadratic form to subspace...

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Postive-Definiteness

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