## Linear Algebra and Its Applications

Published in Linear Algebra and Its Applications

Published in Linear Algebra and Its Applications

Published in Linear Algebra and Its Applications

We obtain upper bounds for the number of arbitrary and symmetric matrices with integer entries in a given box (in an arbitrary location) and a given determinant. We then apply these bounds to estimate the number of matrices in such boxes which have an integer eigenvalues. Finally, we outline some open questions.

Published in Linear Algebra and Its Applications

It is known that for any nonzero complex n×n matrices X and Y the quotient of Frobenius norms‖XY-YX‖F‖X‖F‖Y‖Fdoes not exceed 2. However, except for some special cases, only necessary conditions for attaining this bound have been found so far. We will completely characterize the pairs of matrices that satisfy equality with the quotient’s maximum.

Published in Linear Algebra and Its Applications

Let V be a complex inner product space of positive dimension m with inner product 〈·,·〉, and let Tn(V) denote the set of all n-linear complex-valued functions defined on V×V×⋯×V (n-copies). By Sn(V) we mean the set of all symmetric members of Tn(V). We extend the inner product, 〈·,·〉, on V to Tn(V) in the usual way, and we define multiple tensor pr...

Published in Linear Algebra and Its Applications

The relations between the kernels, as well as the cokernels, of Toeplitz operators are studied in connection with certain relations between their symbols. These results are used to obtain some Fredholm type properties for operators with 2×2 symbols, whose determinant admits a bounded Wiener–Hopf factorization.

Published in Linear Algebra and Its Applications

This paper develops a novel linear system based approach for computing ‖A-1‖∞, the Skeel condition number of an M-matrix A, and the positive diagonal matrices D guaranteeing that AD be a strictly diagonally dominant matrix. Theoretic analysis and simulation results justify the validity of the proposed approach. Moreover, the proposed linear system ...

Published in Linear Algebra and Its Applications

We characterize essential normality for certain elementary operators acting on the Hilbert-Schmidt class. We find the Aluthge transform of an elementary operator of length one. We show that the Aluthge transform of an elementary 2-isometry need not be a 2-isometry. We also characterize hermitian elementary operators of length 2.

Published in Linear Algebra and Its Applications

Let A be a prime ring of characteristic not 2, with center Z(A) and with involution *. Let S be the set of symmetric elements of A. Suppose that f:S→A is an additive map such that [f(x),f(y)]=[x,y] for all x,y∈S. Then unless A is an order in a 4-dimensional central simple algebra, there exists an additive map μ:S→Z(A) such that f(x)=x+μ(x) for all ...

Published in Linear Algebra and Its Applications

In this paper, we first introduce the m-arithmetic triangle which is a generalization of Pascal’s triangle. Then, we put forward some computational results on the evaluations of determinants of matrices related to it. We also try to find the inverse matrix and some factorizations of this type of matrices.

Published in Linear Algebra and Its Applications

We determine and compare the convergence rates of various fixed-point iterations for finding the minimal positive solution of a class of nonsymmetric algebraic Riccati equations arising in transport theory.