# 1233

## Автор(ов):

2

Параметры публикации

## Тип публикации:

Статья в журнале/сборнике

## Название:

On the Spectra of Nonsymmetric Laplacian Matrice

0024-3795

## Наименование источника:

• Linear Algebra and its Applications

V. 399

• Amsterdam

• Elsevier

2005

## Страницы:

157–168
Аннотация
A Laplacian matrix, $L=(\l_{ij})\in\R^{n\times n}$, has nonpositiveoff-diagonal entries and zero row sums.As a matrix associated with a weighted directed graph, it generalizes theLaplacian matrix of an ordinarygraph. A standardized Laplacian matrix is a Laplacian matrix with $-{1\overn}\le\l_{ij}\le0$ at $j\ne i.$ Westudy the spectra of Laplacian matrices and relations between Laplacianmatrices and stochastic matrices. Weprove that the standardized Laplacian matrices $\LT$ are semiconvergent. Themultiplicities of $0$ and $1$ asthe eigenvalues of $\LT$ are equal to the in-forest dimension of thecorresponding digraph and one less thanthe in-forest dimension of the complementary digraph, respectively. Welocalize the spectra of thestandardized Laplacian matrices of order $n$ and study the asymptoticproperties of the corresponding domain.One corollary is that the maximum possible imaginary part of an eigenvalueof $\LT$ converges to${1\over\pi}$ as $n\to\infty.$

## Библиографическая ссылка:

Агаев Р.П., Чеботарев П.Ю. On the Spectra of Nonsymmetric Laplacian Matrice // Linear Algebra and its Applications. 2005. V. 399. С. 157–168.