A two player game (or more correctly, a two player normal-form game) is specified by two m × n payoff matrices R and C corresponding to the row and column player respectively. Each of these matrices has m rows corresponding to the m strategies of the row player and n columns corresponding to the n strategies of the column payer. The row player picks a row i ∈ [m], and the column player picks a ...

‎The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$‎, ‎to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$‎. ‎If there exists an $ntimes n$ symmetric doubly stochastic ...

We prove that perceptrons separating Boolean matrices in which each row has a one from matrices in which many rows have no one must have either large total weight or large order. This result extends one-in-a-box theorem by Minsky and Papert 13] stating that perceptrons of small order cannot decide if each row of a given Boolean matrix has a one. As a consequence, we prove that AM \ co-AM 6 6 PP...

In a previous paper, we introduced reflection equations for interaction-rounda-face (IRF) models and used these to construct commuting double-row transfer matrices for solvable lattice spin models with fixed boundary conditions. In particular, for the Andrews-Baxter-Forrester (ABF) models, we derived special functional equations satisfied by the eigenvalues of the commuting double-row transfer ...

This paper is a continuation of the work done to understand the security of a MOR cryptosystem over matrix groups defined over a finite field. In this paper we show that in the case of unitary group U(d, q) the security of the MOR cryptosystem is similar to the hardness of the discrete logarithm problem in Fq2d . In our way of developing the MOR cryptosystem, we developed row-column operations ...

We prove necessary and sufficient conditions for the existence of sequences and matrices with elements in given intervals and with prescribed lower and upper bounds on the element sums corresponding to the sets of an orthogonal pair of partitions. We use these conditions to generalize known results on the existence of nonnegative matrices with a given zero pattern and prescribed row and column ...

We consider designing a sparse sensing matrix which contains few non-zero entries per row for compressive sensing (CS) systems. By unifying the previous approaches for optimizing sensing matrices based on minimizing the mutual coherence, we propose a general framework for designing a sparse sensing matrix that minimizes the mutual coherence of the equivalent dictionary and is robust to sparse r...

Orthogonal matrices over arbitrary elds are de ned together with their non-square analogs, which are termed row-orthogonal matrices. Antiorthogonal and self-orthogonal square matrices are introduced together with their non-square analogs. The relationships of these matrices to such codes as self-dual codes and linear codes with complementary duals are given. These relationships are used to obta...

Let $mathbf{c}_0$ be the real vector space of all real sequences which converge to zero. For every $x,yin mathbf{c}_0$, it is said that $y$ is block diagonal majorized by $x$ (written $yprec_b x$) if there exists a block diagonal row stochastic matrix $R$ such that $y=Rx$. In this paper we find the possible structure of linear functions $T:mathbf{c}_0rightarrow mathbf{c}_0$ preserving $prec_b$.

We study the ergodicity of backward product of stochastic and doubly stochastic matrices by introducing the concept of absolute infinite flow property. We show that this property is necessary for ergodicity of any chain of stochastic matrices, by defining and exploring the properties of a rotational transformation for a stochastic chain. Then, we establish that the absolute infinite flow proper...