Iterative Methods for Eigenvalues/Eigenvectors

Synonyms

Eigenvalue and eigenvector – characteristic value and characteristic vector; Eigenvalue with the largest magnitude – dominant eigenvalue; Nonsingular – invertible; Vertex: Node

Glossary

Eigenvalue/Eigenvector:

The fundamental entities that characterize any given matrix and can be obtained by finding the roots of the characteristic polynomial of the matrix or by iterative methods

Social Network Analysis:

A research area in social and behavioral sciences that uses networks to represent and hence analyze social phenomena

Iterative Method:

A procedure for solving a problem by generating a sequence of improving approximations to the true solution of the given problem

Definition

Eigenvalues and eigenvectors are fundamental concepts in linear algebra (Golub and Van Loan 2012; Golub and Vorst 2000) and are defined as follows:

Definition 1

Let A be an n-by-n real matrix (i.e., in ${\mathbb{R}}^{n\times n}$). If there exist a scalar $\lambda \in \mathbb{C}$ and a nonzero vector \...