The Kronecker Product SVD
C. Van Loan (CS, Cornell)

If A is a p-by-q block matrix with r-by-s blocks, then it can be written as an SVD-style sum of Kronecker products sigma_1*kron(B_1,C_1) + ... + sigma_r*kron(B_r,C_r) where r is the Kronecker product rank of A.
The B's are p-by-q and the C's are r-by-s.

Originally developed as an avenue for generating effective preconditioners, the 'KSVD' turns out to have interesting applications in computational multilinear algebra.