What is the correct definition of the standard inner product of two given matrices?

Dec 28, 2017 · An inner product is a binary function on a vector space (i.e. it takes two inputs from the vector space) which outputs a scalar, and which satisfies some other axioms (positive …

For intuition, note that $tr (B^T A)$ is what you'd get if you reshaped $A$ and $B$ into column vectors and took the standard inner product.

Mar 13, 2021 · The Frobenius inner product is a way to extend the concept of the dot product from vectors to matrices and it provides a measure of similarity between two matrices, just as the …

Jun 27, 2021 · The inner product between two vectors is the product of length of first vector and the length of projection of second vector on to the first vector. When I take an outer product its …

Mar 30, 2020 · that is, the trace of the product of two matrices is equal to their frobenius inner product, which in turn is the induced inner product on the tensor product of Hilbert spaces.

May 31, 2017 · The standard inner product between matrices is often chosen to be \begin {align} \langle A,B\rangle=\mathrm {tr} (AB^\intercal)\,. \end {align} I would like to define another …

Long story short, the question is simple. Is matrix multiplication just a special case of the dot product of two sets of vectors when the sets of vectors have the same cardinality and all …

Apr 2, 2013 · Hopefully this response will help others. The "double inner product" and "double dot product" are referring to the same thing- a double contraction over the last two indices of the …

Feb 27, 2012 · The product of two positive definite matrices is not necessarily positive definite. The product in most cases is not even symmetric and for sure, it is not positive definite.