Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation.
Flocks in universal and Boolean algebras
We propose the notion of flocks, which formerly were introduced only in based algebras, for any universal algebra. This generalization keeps the main properties we know from vector spaces, e.g. a closure system that extends the subalgebra one. It comes from the idempotent elementary functions, we call "interpolators", that in case of vector spaces merely are linear functions with normalized coefficients. The main example, we consider outside vector spaces, concerns Boolean algebras,...
Formalization of Integral Linear Space
In this article, we formalize integral linear spaces, that is a linear space with integer coefficients. Integral linear spaces are necessary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm that outputs short lattice base and cryptographic systems with lattice [8].
Full rank factorization and the Flanders theorem.
Further results on the reverse order law for -inverse and -inverse of a matrix product.
Generalized inverses of bordered matrices.
Gens de
Geometric structure of positive bases in linear spaces
Graphs whose minimal rank is two.
Graphs whose minimal rank is two: the finite fields case.
Grassmann formula for certain type of modules
Hankel-matrix approach to invertibility of linear multivariable systems
Homomorphisms for Distributive Operations in Partial Algebras. Applications to Linear Operators and Measure Theory.
How to characterize commutativity equalities for Drazin inverses of matrices
Necessary and sufficient conditions are presented for the commutativity equalities , , , and so on to hold by using rank equalities of matrices. Some related topics are also examined.
Independence structures in the geometry of orders.
Inertia sets for graphs on six or fewer vertices.
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,...
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.
Invertible commutativity preservers of matrices over max algebra
The max algebra consists of the nonnegative real numbers equipped with two binary operations, maximization and multiplication. We characterize the invertible linear operators that preserve the set of commuting pairs of matrices over a subalgebra of max algebra.
Join Operations in Vector Spaces.