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trace(AB*) = ? in summation form

* = adjoint = conjugate and transpose = transpose and conjugate

assume both matrices are square mx of same size n x n

trace = sum of diagonal entries

i'm got this after brute force

(summation of this entire thing) a_ij x conjugate of (b_ij)

i, j runs from 1 to n

but somehow i'm thinking it should be

(summation of this entire thing) a_ii x conjugate of (b_ii)

i runs from 1 to n