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A canonical directly infinite ring

Mario Petrich, Pedro V. Silva (2001)

Czechoslovak Mathematical Journal

Let be the set of nonnegative integers and the ring of integers. Let be the ring of N × N matrices over generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of yields that the subrings generated by them coincide. This subring is the sum of the ideal consisting of...

A computation of positive one-peak posets that are Tits-sincere

Marcin Gąsiorek, Daniel Simson (2012)

Colloquium Mathematicae

A complete list of positive Tits-sincere one-peak posets is provided by applying combinatorial algorithms and computer calculations using Maple and Python. The problem whether any square integer matrix A ( ) is ℤ-congruent to its transpose A t r is also discussed. An affirmative answer is given for the incidence matrices C I and the Tits matrices C ̂ I of positive one-peak posets I.

A Fiedler-like theory for the perturbed Laplacian

Israel Rocha, Vilmar Trevisan (2016)

Czechoslovak Mathematical Journal

The perturbed Laplacian matrix of a graph G is defined as L D = D - A , where D is any diagonal matrix and A is a weighted adjacency matrix of G . We develop a Fiedler-like theory for this matrix, leading to results that are of the same type as those obtained with the algebraic connectivity of a graph. We show a monotonicity theorem for the harmonic eigenfunction corresponding to the second smallest eigenvalue of the perturbed Laplacian matrix over the points of articulation of a graph. Furthermore, we use...

A Hadamard product involving inverse-positive matrices

Gassó Maria T., Torregrosa Juan R., Abad Manuel (2015)

Special Matrices

In this paperwe study the Hadamard product of inverse-positive matrices.We observe that this class of matrices is not closed under the Hadamard product, but we show that for a particular sign pattern of the inverse-positive matrices A and B, the Hadamard product A ◦ B−1 is again an inverse-positive matrix.

A linear programming based analysis of the CP-rank of completely positive matrices

Yingbo Li, Anton Kummert, Andreas Frommer (2004)

International Journal of Applied Mathematics and Computer Science

A real matrix A is said to be completely positive (CP) if it can be decomposed as A = BB^T, where the real matrix B has exclusively non-negative entries. Let k be the rank of A and Φ_k the least possible number of columns of the matrix B, the so-called completely positive rank (cp-rank) of A. The present work is devoted to a study of a general upper bound for the cp-rank of an arbitrary completely positive matrix A and its dependence on the ordinary rank k. This general upper bound of the cp-rank...

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