Results 1 to 10 of about 218 (36)

On idempotent stable range 1 matrices

open access: yesSpecial Matrices, 2022
We characterize the idempotent stable range 1, 2 × 2 matrices over commutative rings and in particular the integral matrices with this property. Several special cases and examples complete the subject.
Călugăreanu Grigore, Pop Horia F.
doaj   +1 more source

On the smallest singular value in the class of unit lower triangular matrices with entries in [−a, a]

open access: yesSpecial Matrices, 2021
Given a real number a ≥ 1, let Kn(a) be the set of all n × n unit lower triangular matrices with each element in the interval [−a, a]. Denoting by λn(·) the smallest eigenvalue of a given matrix, let cn(a) = min {λ n(YYT) : Y ∈ Kn(a)}.
Altınışık Ercan
doaj   +1 more source

Generating functions for a lattice path model introduced by Deutsch

open access: yesSpecial Matrices, 2021
The lattice path model suggested by E. Deutsch is derived from ordinary Dyck paths, but with additional down-steps of size −3, −5, −7, . . . . For such paths, we find the generating functions of them, according to length, ending at level i, both, when ...
Prodinger Helmut
doaj   +1 more source

On Generalized Jacobsthal and Jacobsthal–Lucas Numbers

open access: yesAnnales Mathematicae Silesianae, 2022
Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers.
Bród Dorota, Michalski Adrian
doaj   +1 more source

Some combinatorial matrices and their LU-decomposition

open access: yesSpecial Matrices, 2020
Three combinatorial matrices were considered and their LU-decompositions were found. This is typically done by (creative) guessing, and the proofs are more or less routine calculations.
Prodinger Helmut
doaj   +1 more source

Negative clean rings

open access: yesAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022
A ring is called negative clean if the negative (i.e., the additive inverse) of each clean element is also clean. Clean rings are negative clean.
Călugăreanu Grigore, Pop Horia F.
doaj   +1 more source

Maximal Green Sequences of Exceptional Finite Mutation Type Quivers [PDF]

open access: yes, 2014
Maximal green sequences are particular sequences of mutations of quivers which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-C\'ordova-Vafa in the context of supersymmetric gauge theory.
Seven, Ahmet I.
core   +4 more sources

The integer cp-rank of 2 × 2 matrices

open access: yesSpecial Matrices, 2019
We show the cp-rank of an integer doubly nonnegative 2 × 2 matrix does not exceed 11.
Laffey Thomas, Šmigoc Helena
doaj   +1 more source

A generalization of Alternating Sign Matrices [PDF]

open access: yes, 2013
In alternating sign matrices the first and last nonzero entry in each row and column is specified to be +1. Such matrices always exist. We investigate a generalization by specifying independently the sign of the first and last nonzero entry in each row
Brualdi, Richard A., Kim, Hwa Kyung
core   +1 more source

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