Characterizations of Jacobi sign regular matrices

Accurate eigenvalues of certain sign regular matrices

We present a new O(n3) algorithm for computing all eigenvalues of certain sign regular matrices to high relative accuracy in floating point arithmetic. The accuracy and cost are unaffected by the conventional eigenvalue condition numbers. A matrix is called sign regular when the signs of its nonzero minors depend only of the order of the minors. The sign regular matrices we consider are the one...

E-Clean Matrices and Unit-Regular Matrices

Let $a, b, k,in K$ and $u, v in U(K)$. We show for any idempotent $ein K$, $(a 0|b 0)$ is e-clean iff $(a 0|u(vb + ka) 0)$ is e-clean and if $(a 0|b 0)$ is 0-clean, $(ua 0|u(vb + ka) 0)$ is too.

Jacobi Matrices and Boundary Value Problems in Distance-regular Graphs∗

In this work we analyze regular boundary value problems on a distance-regular graph associated with Schrödinger operators. These problems include the cases in which the boundary has two or one vertices. Moreover, we obtain the Green matrix for each regular problem. In each case, the Green matrices are given in terms of two families of orthogonal polynomials one of them corresponding with the di...

Two modified Jacobi methods for M-matrices

GENERALIZED REGULAR FUZZY MATRICES

In this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. This leads to the characterization of a matrix for which the regularity index and the index are identical. Further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.