Our results extend Hong's and Tan's theorems and also provide further evidences to the conjectures of Hong raised in 2008.doi:10.1080/03081087.2010.526942Xu, JiehongLi, MaoGordon and Breach Science PublishersLinear and Multilinear AlgebraJ. Xu, M. Li, Divisibility among power GCD matrices and ...
As N was raised, the estimation bias reduced for all αi’s except for α1 (highlighted values using a) and their standard errors reduced consistently. The behavior of the biases and standard errors is similar irrespective of the type of Mi’s (AR, CS and AR–CS) used. The L1 norms ...
What is the cofactor of a 2x2 matrix? In a two by two matrix, the cofactor of an entry is calculatedby multiplying the following two factors. The negative one raised to the power of sum of the number of the row and the number of the column of the corresponding element. ...
Sequences of structured matrices of increasing size, such as generalized locally Toeplitz sequences, arise in many scientific applications and especially in the numerical discretization of linear differential problems. We assume that the eigenvalues of a matrixX_n, belonging to a sequence of such kind...
This partially solves an open question raised by Hong. Furthermore, we show that such factorization holds if S is a gcd-closed set such that each element is a prime power or the product of two distinct primes, and in particular if S is a gcd-closed set with every element less than 12...
However, the main issue connected to swap algorithms is that they do not ensure robust results for large matrices unless the number of swaps is raised to a number that makes computation itself rather impractical. To provide support to their observations, Fayle and Manica17 performed some tests ...
For instance, the moments of order 2K scale, for unitary invariant ensembles, as the density of eigenvalues raised to the power K-2; the prefactor turns out to be a universal number, i.e. it is independent of the specific probability distribution. An equivalent behaviour and prefactor had ...
awhen federal agents showed up at Diane Monson's house in Butte County,California in August 2002,seeking to destroy her six home-grown marijuana plants,and agents in Oregon sought to prevent Dr.Peter A.Rasmussen and pharmacist David M.Hochhalter phusician-assisted suicides,both cases raised ...
A question whether such matrices exist for all even orders is raised [10, Question 12, p. 419]. There are theorems giving higher-dimensional Hadamard matrices from lower-dimensional ones, for example [10, Theorem 6.1.5]: Theorem 1.2 If h:{1,…,v}n→{−1,1} is an n-dimensional ...
[62] and the results of [63], which state that partition functions of Seiberg-Witten theories in the Ω-background (which are related to topological strings by geometric engineering) are reproduced by matrix models with β-deformed measure (i.e., with Vandermonde determinant raised to the ...