[Research] A question on a matrix equation

[Tzu-Kuo Huang]

Dear all,

 

Recently I came across a matrix equation:

 

QQ' = Q'Q

 

where Q is a square matrix and Q' is its transpose.

This equation is satisfied when Q is symmetric or orthogonal.

My question is: Can this equation be satisfied by a Q that is not symmetric
nor orthogonal?

Any thoughts, pointers, or suggestions are appreciated!

 

Many thanks,

TK

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