This paper has two purposes. Firstly, the paper is devoted to collecting basic facts about the Floquet theorem and various Floquet factorization algorithms claimed for finite-dimensional linear continuous-time periodic (FDLCP) systems. Secondly, the paper presents a unified representation framework for various Floquet factorizations in FDLCP systems, while structural and analytic characteristic...

In this paper we describe three different variations of prime ideals: strongly irreducible ideals, ideals and insulated in the context Leavitt path algebras. We give necessary sufficient conditions under which a proper ideal algebra L is product as well an intersection finitely many these types ideals. Such factorizations, when they are irredundant, shown to be unique except for order factors. ...

The main purpose of this paper is to revisit the internal/simultaneous/robust stabilization problems without assuming the existence of doubly coprime factorizations for the transfer matrices. Indeed, it has been recently shown in the literature that an internally stabilizable does not generally admit doubly coprime factorizations. Firstly, we give new necessary and sufficient conditions for int...

An alternating sign matrix is a square matrix satisfying (i) all entries are equal to 1, −1 or 0; (ii) every row and column has sum 1; (iii) in every row and column the non-zero entries alternate in sign. The 8-element group of symmetries of the square acts in an obvious way on square matrices. For any subgroup of the group of symmetries of the square we may consider the subset of matrices inva...

We present a novel approach to collaborative prediction, using low-norm instead of low-rank factorizations. The approach is inspired by, and has strong connections to, large-margin linear discrimination. We show how to learn low-norm factorizations by solving a semi-definite program, and discuss generalization error bounds for them.

The purpose of this paper is to give new necessary and sufficient conditions for internal stabilizability and existence of left/right/doubly coprime factorizations for linear MIMO systems. In particular, we generalize the YoulaKučera parametrization of all stabilizing controllers for every internally stabilizable MIMO plant which does not necessarily admit doubly coprime factorizations.

The textit{QIF}  (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ}  factorization. The  WZ factorization can be faster than the textit{LU} factorization  because,  it performs the simultaneous evaluation of two columns or two rows. Here, we present a  method for computing the real and integer textit{WZ} and  textit{ZW} factoriz...

In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial factor and factorizations. The first algorithm is conceptually simpler but may require a high degree of the polynomial factor. The second algorithm gives an op...

We construct seven new examples of perfect one-factorizations, in the complete graphs K170, K730. K1370. K1850t and K3126. These are generated by twoand four-quotient starters in finite fields. We also find several examples of perfect one-factorizations that are not isomorphic to previously known examples.

Polynomial maps attached to polynomials of an Ore extension are naturally defined. In this setting we show the importance of pseudo-linear transformations and give some applications. In particular, factorizations of polynomials in an Ore extension over a finite field Fq[t; θ], where θ is the Frobenius automorphism, are translated into factorizations in the usual polynomial ring Fq[x].