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Wyświetlanie 1-15 z 53
Tytuł:
Intervals of certain classes of Z-matrices
Autorzy:
Kannan, M.
Sivakumar, K.
Powiązania:
https://bibliotekanauki.pl/articles/729209.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
interval matrix
M-matrix
N-matrix
N₀-matrix
nonnegativity
Opis:
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.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2014, 34, 1; 85-93
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the matrix form of Kronecker lemma
Autorzy:
da Silva, João
Oliveira, António
Powiązania:
https://bibliotekanauki.pl/articles/729968.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
matrix Kronecker lemma
matrix analysis
convergence
Opis:
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.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2009, 29, 2; 233-243
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some remarks on operators preserving partial orders of matrices
Autorzy:
Hauke, Jan
Powiązania:
https://bibliotekanauki.pl/articles/729966.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
star partial ordering
minus partial ordering
löwner partial ordering
sharp partial order
nonnegative definite matrix
Hermitian matrix
EP-matrix
power of a matrix
polynomial of a matrix
Opis:
Stępniak [Linear Algebra Appl. 151 (1991)] considered the problem of equivalence of the Löwner partial order of nonnegative definite matrices and the Löwner partial order of squares of those matrices. The paper was an important starting point for investigations of the problem of how an order between two matrices A and B from different sets of matrices can be preserved for the squares of the corresponding matrices A² and B², in the sense of the Löwner partial ordering, the star partial ordering, the minus partial ordering, and the sharp partial ordering. Many papers have since been published (mostly coauthored by J.K. Baksalary - to whom the present paper is dedicated) that generalize the results in two directions: by widening the class of matrices considered and by replacing the squares by arbitrary powers. In the present paper we make a résumé of some of these results and suggest some further generalizations for polynomials of the matrices considered.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2008, 28, 1; 143-155
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The asymptotic trace norm of random circulants and the graph energy
Autorzy:
Koshkin, Sergiy
Powiązania:
https://bibliotekanauki.pl/articles/729702.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
random matrix
graph energy
matrix energy
circulant
Toeplitz matrix
band matrix
Dirichlet kernel
non-uniform Berry-Esseen estimate
Talagrand concentration inequality
Opis:
We compute the expected normalized trace norm (matrix/graph energy) of random symmetric band circulant matrices and graphs in the limit of large sizes, and obtain explicit bounds on the rate of convergence to the limit, and on the probabilities of large deviations. We also show that random symmetric band Toeplitz matrices have the same limit norm assuming that their band widths remain small relative to their sizes. We compare the limit norms across a range of related random matrix and graph ensembles.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2016, 36, 1-2; 67-92
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An inverse matrix of an upper triangular matrix can be lower triangular
Autorzy:
Hołubowski, Waldemar
Powiązania:
https://bibliotekanauki.pl/articles/729021.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
upper tringular invertible matrix
group of matrices
Dedekind-finite ring
Opis:
In this note we explain why the group of n×n upper triangular matrices is defined usually over commutative ring while the full general linear group is defined over any associative ring.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2002, 22, 2; 161-166
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Boolean matrices ... neither Boolean nor matrices
Autorzy:
Ricci, Gabriele
Powiązania:
https://bibliotekanauki.pl/articles/728832.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
universal matrix
functional application
generalized matrix
analytic monoid
Opis:
Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we "show" that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A minor modification of this standard definition might fix it.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 1; 141-151
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the matrix negative Pell equation
Autorzy:
Grytczuk, Aleksander
Kurzydło, Izabela
Powiązania:
https://bibliotekanauki.pl/articles/728746.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
the matrix negative Pell equation
powers matrices
Opis:
Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries.
We give necessary and suficient conditions for solvability of the matrix negative Pell equation
(P) X² - dY² = -I with d ∈ N
for nonsingular X,Y belonging to M₂(Z) and his generalization
(Pn) $∑_{i=1}^{n} X₂_{i} - d ∑_{i=1}^{n} Y²_{i} = -I$ with d ∈ N
for nonsingular $X_{i},Y_{i} ∈ M₂(Z)$, i=1,...,n.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2009, 29, 1; 35-45
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Order unicyclic graphs according to spectral radius of unoriented laplacian matrix
Autorzy:
Fan, Yi-Zheng
Wu, Song
Powiązania:
https://bibliotekanauki.pl/articles/743077.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
unicyclic graph
Laplacian matrix
spectral radius
Opis:
The spectral radius of a graph is defined by that of its unoriented Laplacian matrix. In this paper, we determine the unicyclic graphs respectively with the third and the fourth largest spectral radius among all unicyclic graphs of given order.
Źródło:
Discussiones Mathematicae Graph Theory; 2008, 28, 3; 487-499
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Norm estimates for solutions of matrix equations AX-XB=C and X-AXB=C
Autorzy:
Gil', Michael
Powiązania:
https://bibliotekanauki.pl/articles/729497.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
matrix equations
norm estimates
perturbations
invariant subspaces
Opis:
Let A, B and C be matrices. We consider the matrix equations Y-AYB=C and AX-XB=C. Sharp norm estimates for solutions of these equations are derived. By these estimates a bound for the distance between invariant subspaces of matrices is obtained.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 2; 191-206
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized matrix graphs and completely independent critical cliques in any dimension
Autorzy:
Lattanzio, John
Zheng, Quan
Powiązania:
https://bibliotekanauki.pl/articles/743260.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
matrix graph
chromatic number
critical clique
completely independent critical cliques
double-critical conjecture
Opis:
For natural numbers k and n, where 2 ≤ k ≤ n, the vertices of a graph are labeled using the elements of the k-fold Cartesian product Iₙ × Iₙ × ... × Iₙ. Two particular graph constructions will be given and the graphs so constructed are called generalized matrix graphs. Properties of generalized matrix graphs are determined and their application to completely independent critical cliques is investigated. It is shown that there exists a vertex critical graph which admits a family of k completely independent critical cliques for any k, where k ≥ 2. Some attention is given to this application and its relationship with the double-critical conjecture that the only vertex double-critical graph is the complete graph.
Źródło:
Discussiones Mathematicae Graph Theory; 2012, 32, 3; 583-602
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Linear operators preserving maximal column ranks of nonbinary boolean matrices
Autorzy:
Song, Seok-Zun
Yang, Sung-Dae
Hong, Sung-Min
Jun, Young-Bae
Kim, Seon-Jeong
Powiązania:
https://bibliotekanauki.pl/articles/728798.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Boolean matrix
semiring
linear operator on matrices
congruence operator on matrices
maximal column rank of a matrix
Boolean rank of a matrix
Opis:
The maximal column rank of an m by n matrix is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over a nonbinary Boolean algebra. We also characterize the linear operators which preserve the maximal column ranks of matrices over nonbinary Boolean algebra.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 2; 255-265
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some comments on the life and publications of Jerzy K. Baksalary (1944-2005)
Autorzy:
Baksalary, Oskar
Styan, George
Powiązania:
https://bibliotekanauki.pl/articles/729932.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
The Adam Mickiewicz University in Poznań
The August Cieszkowski Agricultural University in Poznań
authorship matrix
bibliometrics
biography
generalized inverses of matrices
history of mathematics and statistics in Poland
linear statistical models
matrix equations and inequalities
matrix partial orderings
obituary
rank of a matrix product
Tadeusz Kotarbiński Pedagogical University in Zielona Góra
Zielona Góra University
Opis:
Following some biographical information on Jerzy K. Baksalary (1944-2005) and some comments by Tadeusz Caliński, Oskar Maria Baksalary, and Image Editors-in-Chief: Bryan L. Shader and Hans Joachim Werner, this article continues with personal remarks on the life and publications of Jerzy K. Baksalary by Anita Dobek, R. William Farebrother, Jürgen Groß, Jan Hauke, Radosław Kala, Erkki Liski, Xiaoji Liu, Augustyn Markiewicz, Thomas Mathew, Wiesław Migdałek, Friedrich Pukelsheim, Tarmo Pukkila, Simo Puntanen, C. Radhakrishna Rao, Dietrich von Rosen, George P.H. Styan, Tomasz Szulc, Yongge Tian, Götz Trenkler, Frank Uhlig, Júlia Volaufová, Haruo Yanai, and Fuzhen Zhang. These remarks are followed by a detailed list of Jerzy Baksalary's publications prepared by the editors of this article.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2008, 28, 1; 5-64
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Maximal column rank preservers of fuzzy matrices
Autorzy:
Song, Seok-Zun
Park, Soo-Roh
Powiązania:
https://bibliotekanauki.pl/articles/728725.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
linear operator on matrices
fuzzy matrix
maximal column rank of a matrix
congruence operator on matrices
chain semiring
Opis:
This paper concerns two notions of rank of fuzzy matrices: maximal column rank and column rank. We investigate the difference of them. We also characterize the linear operators which preserve the maximal column rank of fuzzy matrices. That is, a linear operator T preserves maximal column rank if and only if it has the form T(X) = UXV with some invertible fuzzy matrices U and V.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 2; 207-218
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Inverting covariance matrices
Autorzy:
Stępniak, Czesław
Powiązania:
https://bibliotekanauki.pl/articles/729982.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
multi-way classification
cross
hierarchical
balanced
unbalanced
covariance matrix
inverting
Opis:
Some useful tools in modelling linear experiments with general multi-way classification of the random effects and some convenient forms of the covariance matrix and its inverse are presented. Moreover, the Sherman-Morrison-Woodbury formula is applied for inverting the covariance matrix in such experiments.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2006, 26, 2; 163-177
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A semantic construction of two-ary integers
Autorzy:
Ricci, Gabriele
Powiązania:
https://bibliotekanauki.pl/articles/729095.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
universal matrix
analytic monoid
LISP
semantics
jump
Opis:
To binary trees, two-ary integers are what usual integers are to natural numbers, seen as unary trees. We can represent two-ary integers as binary trees too, yet with leaves labelled by binary words and with a structural restriction. In a sense, they are simpler than the binary trees, they relativize. Hence, contrary to the extensions known from Arithmetic and Algebra, this integer extension does not make the starting objects more complex.
We use a semantic construction to get this extension. This method differs from the algebraic ones, mainly because it is able to find equational features of the extended objects. Two-ary integers turn out to form the free algebra corresponding to the Jónsson-Tarski's "paradoxical" equations. This entails that they have a "sum" operation as well as other operations of higher dimensions.
Two-ary integers can provide LISP memories with convenient direct access jumps and the above low complexity hints at feasible hardware implementations.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2005, 25, 2; 165-219
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 53

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