Results 21 to 30 of about 156 (30)

Variations in the sub-defect of doubly substochastic matrices

Special Matrices
The sub-defect of a doubly stochastic matrix AA, denoted as sd(A)=⌈n−sum(A)⌉sd\left(A)=\lceil n-{\rm{sum}}\left(A)\rceil , is defined as the minimum number of rows and columns required to be added to transform the doubly substochastic matrix into a ...
Cao Lei, Eshkaftaki Ali Bayati, Koyuncu Selcuk   +2 more
doaj   +1 more source

Leading Digit Laws on Linear Lie Groups

, 2015
We determine the leading digit laws for the matrix components of a linear Lie group $G$. These laws generalize the observations that the normalized Haar measure of the Lie group $\mathbb{R}^+$ is $dx/x$ and that the scale invariance of $dx/x$ implies the
Manack, Corey, Miller, Steven J.
core   +1 more source

Factorizations of Matrices Over Projective-free Rings [PDF]

, 2014
An element of a ring $R$ is called strongly $J^{\#}$-clean provided that it can be written as the sum of an idempotent and an element in $J^{\#}(R)$ that commute.
Chen, H., Kose, H., Kurtulmaz, Y.
core  

Power Partial Isometry Index and Ascent of a Finite Matrix [PDF]

, 2013
We give a complete characterization of nonnegative integers $j$ and $k$ and a positive integer $n$ for which there is an $n$-by-$n$ matrix with its power partial isometry index equal to $j$ and its ascent equal to $k$.
Gau, Hwa-Long, Wu, Pei Yuan
core  

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
doaj   +1 more source

Tropical totally positive matrices

, 2018
We investigate the tropical analogues of totally positive and totally nonnegative matrices. These arise when considering the images by the nonarchimedean valuation of the corresponding classes of matrices over a real nonarchimedean valued field, like the
Gaubert, Stéphane, Niv, Adi
core   +3 more sources

Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for Polynomial Transforms Based on Induction [PDF]

, 2010
A polynomial transform is the multiplication of an input vector $x\in\C^n$ by a matrix $\PT_{b,\alpha}\in\C^{n\times n},$ whose $(k,\ell)$-th element is defined as $p_\ell(\alpha_k)$ for polynomials $p_\ell(x)\in\C[x]$ from a list $b=\{p_0(x),\dots,p_{n ...
Kovacevic, Jelena, Pueschel, Markus, Sandryhaila, Aliaksei   +2 more
core  

On Optimal Anticodes over Permutations with the Infinity Norm [PDF]

, 2010
Motivated by the set-antiset method for codes over permutations under the infinity norm, we study anticodes under this metric. For half of the parameter range we classify all the optimal anticodes, which is equivalent to finding the maximum permanent of ...
Schwartz, Moshe, Tamo, Itzhak
core  

Idempotents which are products of two nilpotents

Special Matrices
Over any GCD (greatest common divisor) commutative domain we show that the nontrivial 2×22\times 2 idempotent matrices are products of two nilpotent matrices. In order to find explicitly such decompositions, two procedures are described.
Călugăreanu Grigore, Pop Horia F.
doaj   +1 more source

The spectra of random abelian G-circulant matrices

, 2012
This paper studies the asymptotic behavior of eigenvalues of random abelian G-circulant matrices, that is, matrices whose structure is related to a finite abelian group G in a way that naturally generalizes the relationship between circulant matrices and
Meckes, Mark W.
core   +1 more source