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February 13th, 2017, 05:30 AM   #1
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Question Positive definiteness

If A is a symmetric positive definite matrix, B is diagonal matrix and B>0 then
Can we say A-B is positive definite matrix?
If so, please let me know the source.

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Last edited by mkayan; February 13th, 2017 at 05:57 AM.
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February 13th, 2017, 03:42 PM   #2
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definitely not. Take for an example $A = I$ is the identity matrix and $B = 2I$ is twice the identity.
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February 13th, 2017, 04:43 PM   #3
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many thanks.
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