Constraint on M to keep M^T * A * M positive semidefinite?

  • #1
perplexabot
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Hey all! Let me get right to it!
It is given that $$A \succeq 0$$
I need the following to hold for [itex]M[/itex]: $$M^TAM\succeq 0$$

What are the constraints or conditions on [itex]M[/itex] for [itex]M^TAM\succeq 0[/itex] to hold?

Anything would help at this point... I am open to discussion.

Note: It may be worth mentioning that [itex]A[/itex] is a given matrix where as [itex]M[/itex] is variable.

Thank you for reading : )
 
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Answers and Replies

  • #2
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It is always true. For any ##M##.
 
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  • #3
perplexabot
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It is always true. For any ##M##.
Interesting, I think I see why that is. [itex]xM^TAMx \succeq 0 => y^TAy \succeq 0[/itex]

Thanks for the quick answer. I may have a follow up question later :P
 

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