Results 11 to 20 of about 45 (44)

The integer cp-rank of 2 × 2 matrices

Special Matrices, 2019
We show the cp-rank of an integer doubly nonnegative 2 × 2 matrix does not exceed 11.
Laffey Thomas, Šmigoc Helena
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On Generalized Jacobsthal and Jacobsthal-Lucas polynomials

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
In this paper we introduce a generalized Jacobsthal and Jacobsthal-Lucas polynomials, Jh,n and jh,n, respectively, that consist on an extension of Jacobsthal's polynomials Jn(𝑥) and Jacobsthal-Lucas polynomials jn(𝑥).
Catarino Paula, Morgado Maria Luisa
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Fibonacci and Telephone Numbers in Extremal Trees

Discussiones Mathematicae Graph Theory, 2018
In this paper we shall show applications of the Fibonacci numbers in edge-coloured trees. In particular we determine the successive extremal graphs in the class of trees with respect to the number of (A, 2B)-edge colourings.
Bednarz Urszula, Włoch Iwona
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Jacobsons Lemma fails for nil-clean 2 × 2 integral matrices

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020
We show that for two 2 × 2 integral matrices A, B, if the product AB is nil-clean then BA may not be nil-clean. Despite the fact that for many special cases, BA is also nil-clean, we finally found three counterexamples.
Călugăreanu Grigore, Pop Horia F.
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Rank relations between a {0, 1}-matrix and its complement

Open Mathematics, 2018
Let A be a {0, 1}-matrix and r(A) denotes its rank. The complement matrix of A is defined and denoted by Ac = J − A, where J is the matrix with each entry being 1.
Ma Chao, Zhong Jin
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Generalized Pell Equations for 2 × 2 Matrices

Discussiones Mathematicae - General Algebra and Applications, 2017
In this paper we consider the solutions of the generalized matrix Pell equations X2 − dY2 = cI, where X and Y are 2 × 2 matrices over ℤ, d is a non-zero (positive or negative) square-free integer, c is an arbitrary integer and I is the 2 × 2 identity ...
Cohen Boaz
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Inverses and eigenvalues of diamondalternating sign matrices

Special Matrices, 2014
An n × n diamond alternating sign matrix (ASM) is a (0, +1, −1)-matrix with ±1 entries alternatingand arranged in a diamond-shaped pattern. The explicit inverse (for n even) or generalized inverse (for nodd) of a diamond ASM is derived.
Catral Minerva, Lin Minghua, Olesky D. D., van den Driessche P.   +3 more
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1-Sylvester matrices

Special Matrices
A nonzero element aa is called 1-Sylvester in a ring RR, if there exist b,c∈Rb,c\in R such that 1=ab+ca1=ab+ca. In this article, we study such elements, mainly in matrix rings over commutative rings.
Călugăreanu Grigore
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On (k1A1, k2A2, k3A3)-Edge Colourings in Graphs and Generalized Jacobsthal Numbers

Annales Mathematicae Silesianae
In this paper we introduce a new kind of generalized Jacobsthal numbers in a distance sense. We give the identities and matrix representations for them and their connections with the Fibonacci and the Pell numbers. We also describe the interpretations of
Piejko Krzysztof, Trojnar-Spelina Lucyna
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The number of rational points of some classes of algebraic varieties over finite fields

Open Mathematics
Let Fq{{\mathbb{F}}}_{q} be the finite field of characteristic pp and Fq*=Fq\{0}{{\mathbb{F}}}_{q}^{* }\left={{\mathbb{F}}}_{q}\backslash \left\{0\right\}.
Zhu Guangyan, Fang Yingjue, Luo Yuanyuan, Lin Zongbing   +3 more
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