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When is a matrix positive semidefinite? 
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#1
Jan2612, 11:24 AM

P: 381

Hello people,
Im working on a project and this problem came up: I have a symmetric matrix whose elements are complex variables, and i know that this matrix is positive semidefinite. I have to derive a criterion for the matrix's elements, so that if it's satisfied by them then the matrix will be positive semidefinite. Any idea on how to do that? For example, a positive semidefinite matrix has to satisfy some relation that i can use? Maybe its eigenvalues must be nonnegative? I'd really need your help, thanks a lot! John 


#2
Jan2612, 05:27 PM

Math
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PF Gold
P: 39,495

Yes, a matrix is "positive semidefinite" if and only if all of its eigenvalues are nonnegative. You might want to look at this: http://en.wikipedia.org/wiki/Positivedefinite_matrix



#4
Jan2612, 07:03 PM

Engineering
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P: 7,111

When is a matrix positive semidefinite?



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