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)
Famous quotes containing the word product:
“Mans main task in life is to give birth to himself, to become what he potentially is. The most important product of his effort is his own personality.”
—Erich Fromm (19001980)
“Humour is the describing the ludicrous as it is in itself; wit is the exposing it, by comparing or contrasting it with something else. Humour is, as it were, the growth of nature and accident; wit is the product of art and fancy.”
—William Hazlitt (17781830)