- Published 2007

Let A be an n × n real matrix. An eigenvector of A is a vector such that Ax is parallel to x; in other words, Ax = λx for some real or complex number λ. This number λ is called the eigenvalue of A belonging to eigenvector v. Clearly λ is an eigenvalue iff the matrix A − λI is singular, equivalently, iff det(A − λI) = 0. This is an algebraic equation of degree n for λ, and hence has n roots (with multiplicity). The trace of the square matrix A = (Aij) is defined as

@inproceedings{Vesztergombi2007BackgroundMG,
title={Background material Geometric Graph Theory},
author={Katalin Vesztergombi},
year={2007}
}