Matrix Calculus | Matrix Calculus |
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"From too much study, and from extreme passion, cometh madnesse." There is relatively less published pertaining to matrix-valued convex sets and functions. A partial remedy for venturing into hyperdimensional representations, such as the cubix or quartix, is to first vectorize matrices. This device gives rise to the Kronecker product of matrices; a.k.a, direct product or tensor product. One advantage to vectorization is existence of a traditional two-dimensional matrix representation for the second-order gradient of a real function with respect to a vectorized matrix. To disadvantage is a large new but known set of algebraic rules and the fact that its mere use does not generally guarantee two-dimensional matrix representation of gradients. |
