In this paper we present a method to design paraunitary polyphase matrices of critically sampled rational filter banks. The method is based on (P,Q) shift-invariant systems, and so any kind of rational splitting of the frequency spectrum can be achieved using this method. Ideal (P,Q) shift-invariant system with smallest P and Q that map of a band of input spectrum to the output spectrum are obt...

We propose a new method to compute the joint spectral radius and the joint spectral subradius of a set of matrices. We first restrict our attention to matrices that leave a cone invariant. The accuracy of our algorithm, depending on geometric properties of the invariant cone, is estimated. We then extend our method to arbitrary sets of matrices by a lifting procedure, and we demonstrate the eff...

One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...

In 1957, Chandler Davis proved that unitarily invariant convex functions on the space of hermitian matrices are precisely those which are convex and symmetrically invariant on the set of diagonal matrices. We give a simple perturbation theoretic proof of this result. (Davis’ argument was also very short, though based on completely different ideas). Consider an orthogonally invariant function f ...

We consider the set of quadruples of matrices defining singular linear time-invariant dynamical systems and show that there is a one-to-one correspondence between this set and a subset of the set of polynomial matrices of degree two. This correspondence preserves the equivalence relations introduced in both sets (feedback-similarity and strict equivalence): two quadruples of matrices are feedba...

In this paper we settle a weak version of a conjecture (i.e. Conjecture 6) by Mills, Robbins and Rumsey in the paper “Self-complementary totally symmetric plane partitions” J. Combin. Theory Ser. A 42, 277–292. In other words we show that the number of shifted plane partitions invariant under the involution γ is equal to the number of alternating sign matrices invariant under the vertical flip....

Descriptions are given of multiplicative maps on complex and real matrices that leave invariant a certain function, property, or set of matrices: norms, spectrum, spectral radius, elementary symmetric functions of eigenvalues, certain functions of singular values, (p, q) numerical ranges and radii, sets of unitary, normal, or Hermitian matrices, as well as sets of Hermitian matrices with fixed ...

Descriptions are given of multiplicative maps on complex and real matrices that leave invariant a certain function, property, or set of matrices: norms, spectrum, spectral radius, elementary symmetric functions of eigenvalues, certain functions of singular values, (p, q) numerical ranges and radii, sets of unitary, normal, or Hermitian matrices, as well as sets of Hermitian matrices with fixed ...