In this paper, we present new upper and lower bounds for the spectral norms of the r-circulant matrices [Formula: see text] and [Formula: see text] whose entries are the biperiodic Fibonacci and biperiodic Lucas numbers, respectively. Finally, we obtain lower and upper bounds for the spectral norms of Kronecker and Hadamard products of Q and L matrices.

Sufficient conditions are derived for solutions of a general autonomous system of quad-ratic ordinary vector differential equations to exhibit finite escape times. These results are extended to a matrix Riccati-type differential equation using Kronecker matrix products and a "stacking operator". Finally, these results are applied to a class of models used extensively in population dynamics.

A matroid pencil is a pair of linking systems having the same ground sets in common. It provides a combinatorial abstraction of matrix pencils. This paper investigates the properties of matroid pencils analogous to the theory of Kronecker canonical form. As an application, we give a simple alternative proof for a theorem of Murota on power products of linking systems.

We show that the Doob and Hamming graphs are hyper-self-dual. We then show that although the Doob graphs are formally dual to certain Hamming graphs, they are not hyper-dual to them. We do so by showing that Bose-Mesner subalgebras and Kronecker products of Bose-Mesner algebras inherit hyper-duality.

The expectations of random determinants whose entries are real-valued, identically distributed, mean zero, correlated Gaussian random variables are examined using the Kronecker tensor products and some combinatorial arguments. This result is used to derive the expected determinants of X +B and AX +X ′B.