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

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SUMMARY

The discussion centers on the conditions under which the expression Q-1AQ-1 is Hermitian. It is established that if Q is a positive definite matrix and A is any matrix, the product Q-1AQ-1 does not necessarily yield a Hermitian matrix, particularly when Q is the identity matrix and A is non-symmetric. This highlights the importance of matrix properties in determining the Hermitian nature of products.

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td21
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Hi!

Q is positive definite

A is any matrix.

Why Q^{-1}AQ^{-1} is hermitian??
 
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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
 

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