On the Classification of Hermitian Forms.
On the codimension of the variety of symmetric matrices with multiple eigenvalues.
On the coefficients of the max-algebraic characteristic polynomial and equation
No polynomial algorithms are known for finding the coefficients of the characteristic polynomial and characteristic equation of a matrix in max- algebra. The following are proved: (1) The task of finding the max-algebraic characteristic polynomial for permutation matrices encoded using the lengths of their constituent cycles is NP-complete. (2) The task of finding the lowest order finite term of the max-algebraic characteristic polynomial for a matrix can be converted to the assignment problem....
On the composition of nondegenerate quadratic forms with an arbitrary index
On the composition of nondegenerate quadratic forms with an arbitrary index
On the computation of the minimal polynomial of a polynomial matrix
The main contribution of this work is to provide two algorithms for the computation of the minimal polynomial of univariate polynomial matrices. The first algorithm is based on the solution of linear matrix equations while the second one employs DFT techniques. The whole theory is illustrated with examples.
On the computation of the null space of Toeplitz-like matrices.
On the confidence region of a vector parameter
On the connection between Kronecker and Hadamard convolution products of matrices and some applications.
On the construction and the realization of wild monoids
We develop elementary methods of computing the monoid for a directly-finite regular ring . We construct a class of directly finite non-cancellative refinement monoids and realize them by regular algebras over an arbitrary field.
On the construction of explicit solutions to the matrix equation .
On the convergence theory of double -weak splittings of type II
Recently, Wang (2017) has introduced the -nonnegative double splitting using the notion of matrices that leave a cone invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for -weak regular and -nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory for these sub-classes...
On the cover problems of geometric theory
On the -stability problem for real matrices
Vengono discusse delle condizioni sufficienti affinchè una matrice reale delle dimensioni sia diagonalmente (o -) stabile. Esse includono delle ipotesi geometriche (condizioni degli ortanti), e un criterio che generalizza un criterio di Carlson. Inoltre si discute la -stabilità robusta per le matrici reali delle dimensioni
On the Davis-Kahan-Weinberger Solution of the Norm-Preserving Dilation Problem.
On the decidability of semigroup freeness∗
This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of the following two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness problem over the free monoids....
On the decidability of semigroup freeness
This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of the following two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness problem over the free monoids. In 1991, Klarner, Birget and Satterfield proved the undecidability...
On the decidability of semigroup freeness∗
This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of the following two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness problem over the free monoids....
On the decoupling of one class of multivariable systems
On the defining polynomials of maximal real cyclotomic extensions.