On the Definition of a Quadratic Form
On the degree of nilpotency of the radical of relatively free algebras.
On the Degree of the Minimal Polynomial of the Lyapunov Operator.
On the derivatives of the Perron vector
On The Determinant of q-Distance Matrix of a Graph
In this note, we show how the determinant of the q-distance matrix Dq(T) of a weighted directed graph G can be expressed in terms of the corresponding determinants for the blocks of G, and thus generalize the results obtained by Graham et al. [R.L. Graham, A.J. Hoffman and H. Hosoya, On the distance matrix of a directed graph, J. Graph Theory 1 (1977) 85-88]. Further, by means of the result, we determine the determinant of the q-distance matrix of the graph obtained from a connected weighted graph...
On the determinantal inequalities.
On the determinants of some kinds of circulant-type matrices with generalized number sequences
Recently, determinant computation of circulant type matrices with well-known number sequences has been studied, extensively. This study provides the determinants of the RFMLR, RLMFL, RFPrLrR and RLPrFrL circulant matrices with generalized number sequences of second order.
On the diagonalisation of von Neumann regular matrices
On the diagonals of integral matrices
On the dispersions of the polynomial maps over finite fields.
On the divisibility of power LCM matrices by power GCD matrices
Let be a set of distinct positive integers and an integer. Denote the power GCD (resp. power LCM) matrix on having the -th power of the greatest common divisor (resp. the -th power of the least common multiple ) as the -entry of the matrix by (resp. . We call the set an odd gcd closed (resp. odd lcm closed) set if every element in is an odd number and (resp. ) for all . In studying the divisibility of the power LCM and power GCD matrices, Hong conjectured in 2004 that...
On the doubling of quadratic algebras
The concept of doubling, which was introduced around 1840 by Graves and Hamilton, associates with any quadratic algebra 𝓐 over a field k of characteristic not 2 its double 𝓥(𝓐 ) = 𝓐 × 𝓐 with multiplication (w,x)(y,z) = (wy - z̅x,xy̅ + zw). This yields an endofunctor on the category of all quadratic k-algebras which is faithful but not full. We study in which respect the division property of a quadratic k-algebra is preserved under doubling and, provided this is the case, whether the...
On the doubly refined enumeration of alternating sign matrices and totally symmetric self-complementary plane partitions.
On the Drazin index of regular elements
It is known that the existence of the group inverse a # of a ring element a is equivalent to the invertibility of a 2 a − + 1 − aa −, independently of the choice of the von Neumann inverse a − of a. In this paper, we relate the Drazin index of a to the Drazin index of a 2 a − + 1 − aa −. We give an alternative characterization when considering matrices over an algebraically closed field. We close with some questions and remarks.
On the effect of the perturbation of a nonnegative matrix on its Perron eigenvector
On the Effective Computation of the Inertia of a Non-Hermitian Matrix.
On the efficient update of rectangular LU-factorizations subject to low rank modifications.
On the Eigenvalues of some Class of Pseudo-linear Transformations
On the Eigenvalues of Sums of Hermitian Matrices. II.
On the eigenvalues which express antieigenvalues.