Inner Product
For an m-by-n matrix A with complex (or real) entries and * being the conjugate transpose, we have
with equality if and only if A = 0. The assignment
yields an inner product on the space of all complex (or real) m-by-n matrices.
The norm induced by the above inner product is called the Frobenius norm. Indeed it is simply the Euclidean norm if the matrix is considered as a vector of length mn.
It follows that if A and B are positive semi-definite matrices of the same size then
Read more about this topic: Trace (linear Algebra)
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