Is Q^{-1}AQ^{-1} Always Hermitian?

td21 · 2011-06-13T07:14:57+00:00

Hi! Q is positive definite A is any matrix. Why Q^{-1}AQ^{-1} is hermitian??

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td21

Gold Member

Hi!

Q is positive definite

A is any matrix.

Why [itex]Q^{-1}AQ^{-1}[/itex] is hermitian??

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dragonlorder

let Q be identity matrix, and A be a non symmetric matrix
Q is positive definite
but the product of those 3 is not hermitian