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This is related to my previous https://www.physicsforums.com/showthread.php?t=392069"

Let [tex] A=(a_{ij}) [/tex] be a symmetric (i.e., over reals) PSD matrix with the following conditions on Leading Principle Minors (determinant of the submatrix consisting of first i rows and i columns) [tex] A_{ii}[/tex]:

[tex] A_{11}\ge0,~ A_{22}=A_{44}= A_{66}=A_{77}=A_{88}=detA=0 [/tex]

Now the question is can I say (from the above information) that [tex] A_{33}=A_{55}=0 ?[/tex] From "Matrix Analysis" by Horn and Johnson, I guess theInterlacing Inequlitymay be useful...but I don't know much about it. Any help, please.

As usual, will it still valid if I assume A to be hermitian (i.e., over complex) than being symmetric?

Thanks

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# Condition on Leading principle minors of a symmetric Positive semidefinite(PSD) matri

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