Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 5

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych:  Determinant
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Determinant evaluations for binary circulant matrices

100%
Kravvaritis C.
Special Matrices
|
2014
|
tom 2
|
nr 1
EN
Determinant formulas for special binary circulant matrices are derived and a new open problem regarding the possible determinant values of these specific circulant matrices is stated. The ideas used for the proofs can be utilized to obtain more determinant formulas for other binary circulant matrices, too. The superiority of the proposed approach over the standard method for calculating the determinant of a general circulant matrix is demonstrated.
2
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Cullis-Radić determinant of a rectangular matrix which has a number of identical columns

80%
Makarewicz A., Pikuta P.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2020
|
tom 74
|
nr 2
EN
In this paper we present how identical columns affect the Cullis-Radić determinant of an \(m\times n\) matrix, where \(m\leq n\).
3
Content available remote

Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions

80%
Hong S., Hu S., Hong S.
Open Mathematics
|
2016
|
tom 14
|
nr 1
146-155
EN
Let f be an arithmetic function and S = {x1, …, xn} be a set of n distinct positive integers. By (f(xi, xj)) (resp. (f[xi, xj])) we denote the n × n matrix having f evaluated at the greatest common divisor (xi, xj) (resp. the least common multiple [xi, xj]) of x, and xj as its (i, j)-entry, respectively. The set S is said to be gcd closed if (xi, xj) ∈ S for 1 ≤ i, j ≤ n. In this paper, we give formulas for the determinants of the matrices (f(xi, xj)) and (f[xi, xj]) if S consists of multiple coprime gcd-closed sets (i.e., S equals the union of S1, …, Sk with k ≥ 1 being an integer and S1, …, Sk being gcd-closed sets such that (lcm(Si), lcm(Sj)) = 1 for all 1 ≤ i ≠ j ≤ k). This extends the Bourque-Ligh, Hong’s and the Hong-Loewy formulas obtained in 1993, 2002 and 2011, respectively. It also generalizes the famous Smith’s determinant.
4
Content available remote

On characteristic and permanent polynomials of a matrix

70%
Singh R., Bapat R. B.
Special Matrices
|
2017
|
tom 5
|
nr 1
97-112
EN
There is a digraph corresponding to every square matrix over ℂ. We generate a recurrence relation using the Laplace expansion to calculate the characteristic and the permanent polynomials of a square matrix. Solving this recurrence relation, we found that the characteristic and the permanent polynomials can be calculated in terms of the characteristic and the permanent polynomials of some specific induced subdigraphs of blocks in the digraph, respectively. Interestingly, these induced subdigraphs are vertex-disjoint and they partition the digraph. Similar to the characteristic and the permanent polynomials; the determinant and the permanent can also be calculated. Therefore, this article provides a combinatorial meaning of these useful quantities of the matrix theory. We conclude this article with a number of open problems which may be attempted for further research in this direction.
5
Content available remote

Immanant Conversion on Symmetric Matrices

61%
Purificação Coelho M., Duffner M. A., Guterman A. E.
Special Matrices
|
2014
|
tom 2
|
nr 1
EN
Letr Σn(C) denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C) -> Σn (C) satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB) = dχ·(Φ(Α ) + αΦ(Β)) for all matrices A,В ε Σ„(С) and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С).
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.