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

  1. Dec 8, 2015 #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 : )
     
    Last edited: Dec 8, 2015
  2. jcsd
  3. Dec 8, 2015 #2
    It is always true. For any ##M##.
     
  4. Dec 8, 2015 #3

    perplexabot

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    Gold Member

    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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