Matrix Decomposition (2026-04-24)

https://github.com/deleeuw/decomp has R code and paper for matrix decomposition of X in the squared Kronecker norm tr RXCX', with R and C positive semi-definite matrices. Specifically we look at decompositions of the form X = c + ae' + eb' + D. The four components are used to define four Kronecker-orthogonal subspaces of matrix space. We project X on these four subspaces, using the Kronecker metric. We discuss

• applications to matrix approximation,
• generalizations to multidimensional arrays,
• extensions to external or passive variables, and
• ML estimation for the matrix variate normal distribution.