Let $A^*$ denote the complex conjugate transpose of a matrix $A$. In the Euclidean norm, if
$$||A^*A+AA^*||=||A^*A||$$
does it imply that $AA^*=0$. If not, could you give a counter-example?
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For a counterexample, consider $$ A:=\pmatrix{0&1\\0&0}. $$
answered Feb 1 '15 at 13:20
