Displaying similar documents to “Notes on linear combinations of two tripotent, idempotent and involutive matrices that commute.”

Factorizations for q-Pascal matrices of two variables

Thomas Ernst (2015)

Special Matrices

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In this second article on q-Pascal matrices, we show how the previous factorizations by the summation matrices and the so-called q-unit matrices extend in a natural way to produce q-analogues of Pascal matrices of two variables by Z. Zhang and M. Liu as follows [...] We also find two different matrix products for [...]

Nonsingularity and P -matrices.

Jiří Rohn (1990)

Aplikace matematiky

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New proofs of two previously published theorems relating nonsingularity of interval matrices to P -matrices are given.

Intervals of certain classes of Z-matrices

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

Discussiones Mathematicae - General Algebra and Applications

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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.

Block diagonalization

Jaromír J. Koliha (2001)

Mathematica Bohemica

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We study block diagonalization of matrices induced by resolutions of the unit matrix into the sum of idempotent matrices. We show that the block diagonal matrices have disjoint spectra if and only if each idempotent matrix in the inducing resolution double commutes with the given matrix. Applications include a new characterization of an eigenprojection and of the Drazin inverse of a given matrix.

Generalizations of Nekrasov matrices and applications

Ljiljana Cvetković, Vladimir Kostić, Maja Nedović (2015)

Open Mathematics

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In this paper we present a nonsingularity result which is a generalization of Nekrasov property by using two different permutations of the index set. The main motivation comes from the following observation: matrices that are Nekrasov matrices up to the same permutations of rows and columns, are nonsingular. But, testing all the permutations of the index set for the given matrix is too expensive. So, in some cases, our new nonsingularity criterion allows us to use the results already...