Is it true for complex matrices $X,Y$ that $$ (XY)^*=X^* Y^*? $$ where $^*$ refers to complex conjugation. How can we prove this if so? Thanks!
Note: I am referring to complex conjugation, not the hermitan transpose. The answer below refers to hermitan tranpose.
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$\begingroup$For conjugate transpose it holds $(XY)^*=Y^*X^*$, see here.
Edit: For complex conjugation, indeed, $(XY)^*=X^*Y^*$, see here, and the wikipedia article here, section "generalisations".
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