Displaying similar documents to “Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix”

Intervals of certain classes of Z-matrices

M. Rajesh Kannan, K.C. Sivakumar (2014)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.

On the matrix form of Kronecker lemma

João Lita da Silva, António Manuel Oliveira (2009)

Discussiones Mathematicae Probability and Statistics

Similarity:

A matrix generalization of Kronecker's lemma is presented with assumptions that make it possible not only the unboundedness of the condition number considered by Anderson and Moore (1976) but also other sequences of real matrices, not necessarily monotone increasing, symmetric and nonnegative definite. A useful matrix decomposition and a well-known equivalent result about convergent series are used in this generalization.