In Kronecker products works, matrices are some times regarded as vectors and vectors are some times made in to matrices. To be precise about these reshaping we use the vector and diagonal extraction operators. In the present paper, the results are organized in the following ways. First, we formulate the coupled matrix linear least-squares problem and present the efficient solutions of this prob...

In this paper we present a brief overview on Hadamard, KhatriRao, Kronecker and several related non-simple matrix products and their properties. We include practical applications, in different areas, of some of the al-

In this paper we give a combinatorial interpretation for the coefficient of sν in the Kronecker product s(n−p,p) ∗ sλ, where λ = (λ1, . . . , λ`(λ)) ` n, if `(λ) ≥ 2p − 1 or λ1 ≥ 2p − 1; that is, if λ is not a partition inside the 2(p − 1) × 2(p − 1) square. For λ inside the square our combinatorial interpretation provides an upper bound for the coefficients. In general, we are able to combinat...

The Kronecker product is a key algorithm and is ubiquitous across the physical, biological, and computation social sciences. Thus considerations of optimal implementation are important. The need to have high performance and computational reproducibility is paramount. Moreover, due to the need to compose multiple Kronecker products, issues related to data structures, layout and indexing algebra ...

Dedicated to Anders Björner on the occasion of his sixtieth birthday. Abstract The numerical calculation of character values as well as Kronecker coefficients can efficently be carried out by means of character polynomi-als. Yet these polynomials do not seem to have been given a proper role in present day literature or software. To show their remarkable simplicity we give here an " umbral " ver...