Inequalities involving Hadamard products of Hermitian matrices.
Inequalities involving immanants and diagonal products for H-matrices and positive definite matrices
Inequalities involving Khatri-Rao products of positive semi-definite matrices.
Inequalities on the singular values of an off-diagonal block of a Hermitian matrix.
Inertia sets for graphs on six or fewer vertices.
Inertial law of quadratic forms on modules over plural algebra
Quadratic forms on a free finite-dimensional module are investigated. It is shown that the inertial law can be suitably generalized provided the vector space is replaced by a free finite-dimensional module over a certain linear algebra over ( real plural algebra) introduced in [1].
Inertial law of symplectic forms on modules over plural algebra
In this paper the problem of construction of the canonical matrix belonging to symplectic forms on a module over the so called plural algebra (introduced in [5]) is solved.
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.