We offer a detailed examination of a broad class of 2 × 2 matrix games as a first step toward considering measures of resource distribution and efficiency of outcomes. In the present essay, only noncooperative equilibria and entropic outcomes are considered, and a crude measure of efficiency employed. Other solution concepts and the formal construction of an efficiency index will be addressed i...

MDS matrices allow to build optimal linear diffusion layers in block ciphers. However, MDS matrices cannot be sparse and usually have a large description, inducing costly software/hardware implementations. Recursive MDS matrices allow to solve this problem by focusing on MDS matrices that can be computed as a power of a simple companion matrix, thus having a compact description suitable even fo...

This study is motivated by a need to effectively determine the difference between a system fault and normal system operation under parametric uncertainty using eigenstructure analysis. This involves computational robustness of eigenvectors in linear state space systems dependent upon uncertain parameters. The work involves the development of practical algorithms which provide for computable rob...

The standard way of solving the polynomial eigenvalue problem of degree m in n×n matrices is to “linearize” to a pencil in mn×mn matrices and solve the generalized eigenvalue problem. For a given polynomial, P , infinitely many linearizations exist and they can have widely varying eigenvalue condition numbers. We investigate the conditioning of linearizations from a vector space DL(P ) of penci...

Oriented linear graphs have already half a century ago been considered suitable to describe lumped physical systems /1/. Usually matrix equations arising from partial differential equations describing physical networks are very sparse. Companion models arising from linear electrical circuits are introductory presented. /2/. Specific versatile companion model graph eguations can be applied when,...

The Study Companion Android Application is a comprehensive mobile platform designed to enhance the study experience for students and individuals preparing academic competitive exams. application provides user-friendly interface that allows users easily download upload notes related their subjects By centralizing materials in one convenient location, simplifies process of accessing organizing ma...

By means of a proper notion of periodic cyclic matrix, we study the possibility of transforming a given periodic system into a canonical companion form. The passage from such form to an input-output periodic representation is straightforward. We characterize the structural properties of a system in canonical form in terms of coprimeness of the two periodic polynomials appearing in the input-out...

We give simple criteria to identify the exponential order of magnitude absolute value determinant for wide classes random matrix models, not requiring assumption invariance. These include Gaussian matrices with covariance profiles, Wigner and subexponential tails, Erd\H{o}s-R\'enyi $d$-regular graphs any polynomial sparsity parameter, non-mean-field such as band bandwidth. The proof builds on r...