Originally Posted by

**OkashiiKen** Hi all i could use a little help. Thanks in advance.

Prove that if A is Hermitian than (Ax, y) = (x, Ay), where x and y are any vectors.

what ive tried:

(Ax, y) = summation(A.x_i . conj(y_i); i = 1...n)

(x, Ay) = summation(x_i . conj(A . y_i); i =1...n) but A = A* so

(x, Ay) = summation(x_i . conj(A*, y_i); i =1...n) and A* = conj(trans(A))

note*[trans = transpose]

(x, Ay) = summation(x_i . conj(conj(trans(A)), y_i); i =1...n) which can be simplified to

(x, Ay) = summation(x_i . trans(A) . conj(y_i); i =1....n) using distributive property of matrix multiplication

(x, Ay) = summation(trans(A) . x_i . conj(y_i); i =1....n)

I must be missing something because i cannot guarantee A = trans(A) or A = conj(A) i think.

Thanks.