MaplePrimes - answers and comments on Question, Eigenvalues Doesn't Return All The E-Values

quadratic

acer — Tue, 16 Oct 2012 20:14:32 Z

An eigenvalue L of this generalized eigenvalue problem has to satisfy this equation,

> LinearAlgebra:-Determinant(L*LinearAlgebra:-IdentityMatrix(3).G-P) =  0;

                        2
                       L  - L beta - L + beta - kappa L = 0

acer

Reference

Markiyan Hirnyk — Tue, 16 Oct 2012 20:35:07 Z

See "Generalized eigenvalue problem" in the Wiki article http://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix . Another form of the equation is Determinant(P-lambda*G)=0.

PS. Thus, the number of the generalized eigenvalues of two square matrices having dimension N
can be less than N.