Inertially arbitrary nonzero patterns of order 4.
Inertias and ranks of some Hermitian matrix functions with applications
Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively. As applications,...
Inference for random effects in prime basis factorials using commutative Jordan algebras
Commutative Jordan algebras are used to drive an highly tractable framework for balanced factorial designs with a prime number p of levels for their factors. Both fixed effects and random effects models are treated. Sufficient complete statistics are obtained and used to derive UMVUE for the relevant parameters. Confidence regions are obtained and it is shown how to use duality for hypothesis testing.
Infinite dimensional linear groups with a large family of -invariant subspaces
Let be a field, be a vector space over , be the group of all automorphisms of the vector space . A subspace is called almost -invariant, if is finite. In the current article, we begin the study of those subgroups of for which every subspace of is almost -invariant. More precisely, we consider the case when is a periodic group. We prove that in this case includes a -invariant subspace of finite codimension whose subspaces are -invariant.
Infinite divisibility of Smith matrices
Infinite Root Systems, Representations of Graphs and Invariant Theory.
Integer matrices related to Liouville's function
In this note, we construct some integer matrices with determinant equal to certain summation form of Liouville's function. Hence, it offers a possible alternative way to explore the Prime Number Theorem by means of inequalities related to matrices, provided a better estimate on the relation between the determinant of a matrix and other information such as its eigenvalues is known. Besides, we also provide some comparisons on the estimate of the lower bound of the smallest singular value. Such discussion...
Integer sequences and matrices over finite fields.
Integral representation of the Drazin inverse.
Integral representations for multiple Hermite and multiple Laguerre polynomials
We give integral representations for multiple Hermite and multiple Laguerre polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.
Integrity basis for a second-order and a fourth-order tensor.
Interdependence of some problems arising in generalizing the Marcus-de Oliveira determinantal conjecture
Interior points of the completely positive cone.
Interlacing for weighted graphs using the normalized Laplacian.
Interpolation by matrices.
Intertwining of birth-and-death processes
It has been known for a long time that for birth-and-death processes started in zero the first passage time of a given level is distributed as a sum of independent exponentially distributed random variables, the parameters of which are the negatives of the eigenvalues of the stopped process. Recently, Diaconis and Miclo have given a probabilistic proof of this fact by constructing a coupling between a general birth-and-death process and a process whose birth rates are the negatives of the eigenvalues,...
Interval algorithm for absolute value equations
We investigate the absolute value equations Ax−|x| = b. Based on ɛ-inflation, an interval verification method is proposed. Theoretic analysis and numerical results show that the new proposed method is effective.
Interval fuzzy matrix equations
This paper deals with the solvability of interval matrix equations in fuzzy algebra. Fuzzy algebra is the algebraic structure in which the classical addition and multiplication are replaced by maximum and minimum, respectively. The notation , where are given interval matrices and is an unknown matrix, represents an interval system of matrix equations. We can define several types of solvability of interval fuzzy matrix equations. In this paper, we shall deal with four of them. We define the...
Interval solutions of linear interval equations
It is shown that if the concept of an interval solution to a system of linear interval equations given by Ratschek and Sauer is slightly modified, then only two nonlinear equations are to be solved to find a modified interval solution or to verify that no such solution exists.
Intervals of certain classes of Z-matrices
Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.