Background material Geometric Graph Theory


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

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Cite this paper

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