# Browsing Department of Mathematics & Statistics by Title

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• (Department of Mathematics and Statistics, University of Regina, 2004)
• (SIAM, 2009)
Hyperbolic quadratic matrix polynomials $Q(\lambda) = \lambda^2 A + \lambda B + C$ are an important class of Hermitian matrix polynomials with real eigenvalues, among which the overdamped quadratics are those with ...
• (Elsevier, 2015)
The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric n ×n matrix is a sequence from A,S, or N according as all, some, or none of its principal minors of order k are nonzero. Such sequences give ...
• (Elsevier, 2015-08-15)
The enhanced principal rank characteristic sequence (epr-sequence) was originally defined for an n ×n real symmetric matrix or an n ×n Hermitian matrix. Such a sequence is defined to be l1l2···ln where lk is A,S, or N ...
• (SIAM Journal on Discrete Mathematics, 2014)
Let G = PGL(2, q) be the projective general linear group acting on the projec- tive line P_q. A subset S of G is intersecting if for any pair of permutations \pi and \sigma in S, there is a projective point p in P_q such ...
• (European Journal of Combinatorics, 2016)
We prove an analogue of the classical Erdős-Ko-Rado theorem for intersecting sets of permutations in finite $2$-transitive groups. Given a finite group $G$ acting faithfully and $2$-transitively on the set ...
• (SIAM J. Discrete Math. 28, 2014)
In this paper we prove an Erdős-Ko-Rado-type theorem for intersecting sets of permutations. We show that an intersecting set of maximal size in the projective general linear group $PGL_3(q)$, in its natural ...
• (SIAM, 2009)
A 25-year old and somewhat neglected algorithm of Crawford and Moon attempts to determine whether a given Hermitian matrix pair $(A,B)$ is definite by exploring the range of the function $f(x) = x^*(A + iB)x/|x^*(A + ... • (2014-01-21) • (Taylor & Francis, 2013) We start with a discussion of coupled algebraic Riccati equations arising in the study of linear-quadratic optimal control problem for Markov jump linear systems. Under suitable assumptions, this system of equations has ... • (SIAM, 2010) The matrix equation$X+A^TX^{-1}A=Q$has been studied extensively when$A$and$Q$are real square matrices and$Q$is symmetric positive definite. The equation has positive definite solutions under suitable conditions, ... • (International Linear Algebra Society, 2014-06) Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all ... • (2016-06) In this paper we give a proof of the Mikl´os-Manickam-Singhi (MMS) conjecture for some partial geometries. Specifically, we give a condition on partial geometries which implies that the MMS conjecture holds. Further, ... • (International Linear Algebra Society, 2013-09) The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven and then applied to ... • (Springer, 2013) For the algebraic Riccati equation whose four coefficient matrices form a nonsingular$M$-matrix or an irreducible singular$M$-matrix$K$, the minimal nonnegative solution can be found by Newton's method and the doubling ... • (Public Knowledge Network, 2013) We establish the bounds 4 on the Nordhaus- Gaddum sum upper bound multipliers for all graphs G, in connections with certain Colin de Verdi ere type graph parameters. The Nordhaus-Gaddum sum lower bound is conjectured ... • (Elsevier, 2008) The fixed-point iteration is a simple method for finding the maximal Hermitian positive definite solutions of the matrix equations$X\pm A^*X^{-1}A=I$(the plus/minus equations). The convergence of this method ... • (Elsevier, 2012) The Green's function approach for treating quantum transport in nano devices requires the solution of nonlinear matrix equations of the form$X+(C^*+{\rm i} \eta D^*)X^{-1}(C+{\rm i} \eta D)=R+{\rm i}\eta P$, where$R$... • (SIAM, 2012) The matrix equation$X+A^{T}X^{-1}A=Q$arises in Green's function calculations in nano research, where$A$is a real square matrix and$Q$is a real symmetric matrix dependent on a parameter and is usually indefinite. ... • (Elsevier, 2013) We consider the algebraic Riccati equation for which the four coefficient matrices form an$M$-matrix$K$. When$K$is a nonsingular$M$-matrix or an irreducible singular$M\$-matrix, the Riccati equation is known to have ...