# EigensystemOverview

An ordinary linear eigensystem problem is represented by the equation Ax = λx, where A denotes an n x n matrix. The value λ is an eigenvalue, and x ≠ 0 is the corresponding eigenvector. The eigenvector is determined up to a scalar factor. In all functions, this factor is chosen so that x has Euclidean length 1, and the component of x of largest magnitude is positive. If x is a complex vector, this component of largest magnitude is scaled to be real and positive. The entry where this component occurs can be arbitrary for eigenvectors having non-unique maximum magnitude values.

A generalized linear eigensystem problem is represented by Ax = λBx, where A and B are n x n matrices. The value λ is a generalized eigenvalue, and x is the corresponding generalized eigenvector. The generalized eigenvectors are normalized in the same manner as for ordinary eigensystem problems.