Why a^H diag(bb^H)a=b^H diag(aa^H)b,a,b in bbbC^(N xx 1)?

restgarnut 2022-09-12 Answered
Why a H diag ( b b H ) a = b H diag ( a a H ) b , a , b C N × 1 ?
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Answers (1)

Salvador Howard
Answered 2022-09-13 Author has 12 answers
diag ( A ) = i = 1 N e i e i H A e i e i H , where ei is the standard basis of C N
Therefore
a H diag ( b b H ) a = i = 1 N a H e i e i H b b H e i e i H a = i = 1 N b H e i e i H a a H e i e i H b = b H diag ( a a H ) b .
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