EXTENSIONS OF THE REAL MATRIX-VARIATE GAMMA AND BETA FUNCTIONS AND THEIR APPLICATIONS

2017 ◽  
Vol 101 (10) ◽  
pp. 2333-2347
Author(s):  
Gauhar Rahman ◽  
Kottakkaran Sooppy Nisar ◽  
Junesang Choi ◽  
Shahid Mubeen ◽  
Muhammad Arshad
Keyword(s):  
Real Matrix ◽  
The Real

scholarly journals ZPC Matrices and Zero Cycles

2009 ◽  
Vol 2009 ◽  
pp. 1-5
Author(s):  
Marina Arav ◽  
Frank Hall ◽  
Zhongshan Li ◽  
Bhaskara Rao
Keyword(s):  
Real Matrix ◽  
The Real ◽  
Permutation Matrices ◽  
Zero Position ◽  
Common Index

Let H be an m×n real matrix and let Zi be the set of column indices of the zero entries of row i of H. Then the conditions |Zk∩(∪i=1k−1Zi)|≤1 for all k  (2≤k≤m) are called the (row) Zero Position Conditions (ZPCs). If H satisfies the ZPC, then H is said to be a (row) ZPC matrix. If HT satisfies the ZPC, then H is said to be a column ZPC matrix. The real matrix H is said to have a zero cycle if H has a sequence of at least four zero entries of the form hi1j1,hi1j2,hi2j2,hi2j3,…,hikjk,hikj1 in which the consecutive entries alternatively share the same row or column index (but not both), and the last entry has one common index with the first entry. Several connections between the ZPC and the nonexistence of zero cycles are established. In particular, it is proved that a matrix H has no zero cycle if and only if there are permutation matrices P and Q such that PHQ is a row ZPC matrix and a column ZPC matrix.

REAL KM MATRIX AND CABIBBO MATRIX

2001 ◽  
Vol 16 (10) ◽  
pp. 647-654
Author(s):  
CHANDRARAJU CVAVB
Keyword(s):  
Exact Expression ◽  
Real Matrix ◽  
Orthogonal Matrices ◽  
Mixing Angle ◽  
The Real ◽  
Mass Matrices ◽  
Mixing Matrix

Fritzsch type of real symmetric 3×3 matrices are chosen. From these matrices the mass matrices relevant to the four-quark cases are deduced. It is also shown that the orthogonal matrices that diagonalize the 3×3 Fritzsch mass matrices also yield the orthogonal matrices that diagonalize the mass matrices corresponding to the four-quark case. The Cabibbo mixing matrix is straightaway obtained from the KM real mixing matrix. An exact expression for the Cabibbo mixing angle is found here. The real KM matrix is reduced to a few parameters, which can be determined from the experiment. The results obtained here are the exact expressions for the KM real matrix.

scholarly journals 2-Local derivations of real AW*-algebras are derivation

Positivity ◽  
2021 ◽  
Author(s):  
R. A. Dadakhodjaev ◽  
A. A. Rakhimov
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Real Matrix ◽  
Inner Derivation ◽  
The Real ◽  
Matrix Algebras ◽  
Enveloping Algebra ◽  
Local Derivation

Abstract2-Local derivations on real matrix algebras over unital semi-prime Banach algebras are considered. Using the real analogue of the result that any 2-local derivation on the algebra $$M_{2^n}(A)$$ M 2 n ( A ) ($$n\ge 2$$ n ≥ 2 ) is a derivation, it is shown that any 2-local derivation on real AW$$^*$$ ∗ -algebra for which the enveloping algebra is (complex) AW*-algebra, is a derivation, where A is a unital semi-prime Banach algebra with the inner derivation property.

scholarly journals On the Solutions of Some Linear Complex Quaternionic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Cennet Bolat ◽  
Ahmet İpek
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sylvester Equation ◽  
Real Matrix ◽  
Matrix Representations ◽  
Linear Complex ◽  
The Real ◽  
Special Cases ◽  
Necessary And Sufficient

Some complex quaternionic equations in the typeAX-XB=Care investigated. For convenience, these equations were called generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases. By the real matrix representations of complex quaternions, the necessary and sufficient conditions for the solvability and the general expressions of the solutions are obtained.

scholarly journals Central limit theorems for the real eigenvalues of large Gaussian random matrices

2017 ◽  
Vol 06 (01) ◽  
pp. 1750002 ◽  
Author(s):  
N. J. Simm
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Polynomial Function ◽  
Random Variable ◽  
Real Matrix ◽  
Two Component System ◽  
The Real ◽  
Two Component ◽  
Standard Normal ◽  
Independent Identically Distributed

Let [Formula: see text] be an [Formula: see text] real matrix whose entries are independent identically distributed standard normal random variables [Formula: see text]. The eigenvalues of such matrices are known to form a two-component system consisting of purely real and complex conjugated points. The purpose of this paper is to show that by appropriately adapting the methods of [E. Kanzieper, M. Poplavskyi, C. Timm, R. Tribe and O. Zaboronski, Annals of Applied Probability 26(5) (2016) 2733–2753], we can prove a central limit theorem of the following form: if [Formula: see text] are the real eigenvalues of [Formula: see text], then for any even polynomial function [Formula: see text] and even [Formula: see text], we have the convergence in distribution to a normal random variable [Formula: see text] as [Formula: see text], where [Formula: see text].

scholarly journals ON THE REAL MATRIX REPRESENTATION OF PT-SYMMETRIC OPERATORS

2014 ◽  
Vol 54 (2) ◽  
pp. 113-115 ◽  
Author(s):  
Francisco M. Fernández
Keyword(s):  
Matrix Representation ◽  
Real Matrix ◽  
Matrix Representations ◽  
The Real ◽  
Symmetric Operators

We discuss the construction of real matrix representations of PT-symmetric operators. We show the limitation of a general recipe presented some time ago for non-Hermitian Hamiltonians with antiunitary symmetry and propose a way to overcome it. Our results agree with earlier ones for a particular case.

scholarly journals Matrix functions that preserve the strong Perron-Frobenius property

2015 ◽  
Vol 30 ◽  
Author(s):  
Pietro Paparella
Keyword(s):  
Canonical Form ◽  
Matrix Functions ◽  
Real Matrix ◽  
Jordan Canonical Form ◽  
The Real

In this note, matrix functions that preserve the strong Perron-Frobenius property are characterized, using the real Jordan canonical form of a real matrix.

scholarly journals On Hadamard Product of Hypercomplex Numbers

2021 ◽  
Vol 104 (4) ◽  
pp. 68-73
Author(s):  
A. Da¸sdemir ◽  
Keyword(s):  
Hadamard Product ◽  
Matrix Theory ◽  
Real Matrix ◽  
Complex Matrix ◽  
Hypercomplex Numbers ◽  
Matrix Space ◽  
The Real ◽  
Algebraic Properties ◽  
Product Rules ◽  
Analogous Product

Certain product rules take various forms in the set of hypercomplex numbers. In this paper, we introduce a new multiplication form of the hypercomplex numbers that will be called «the Hadamard product», inspired by the analogous product in the real matrix space, and investigate some algebraic properties of that, including the norm of inequality. In particular, we extend our new definition and its applications to the complex matrix theory.

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