Eigenvalues, Multiplicities and Graphs
Eigenvalues, Multiplicities and Graphs
复制标题
特征值、重数和图
DOI：
10.1017/9781316155158
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Carlos M. Saiago
中科院分区：
文献类型：
--
作者：
Charles R. Johnson;Carlos M. Saiago
由矩阵的图形描述的矩阵的非零元素的排列限制了本征值的可能的几何重数，这比代数重数或本征值的数值更受此信息的限制。这本书给出了一个统一的发展如何图的对称矩阵inluences可能的多重性，其特征值。虽然理论是最丰富的情况下，图是一棵树，工作的特征值，多重性和图形提供了机会，以确定哪些想法有类似的非树，和那些树是必不可少的。它收集和组织基本思想，使学生和研究人员能够轻松访问和调查该主题中的许多有趣问题。
The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than are algebraic multiplicities or the numerical values of the eigenvalues. This book gives a uniied development of how the graph of a symmetric matrix inluences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject.