Question: Eigenvalues Doesn't Return All The E-Values

Hi,

I was trying to find the generalized eigenvalues for the (3x3) matrix pair (P,G) defined below. (I have left everything in symbols with beta and kappa both of which are strictly positive real numbers). For some reason the command Eigenvalues(P,G) is only returning 2 generalized eigenvalues. Any ideas why it doesn't return 3?

 

Thanks,

Lee

P := Matrix([[1, 1, 0], [0, -beta, 0], [0, 0, 1]])

G := Matrix([[1, 0, 0], [kappa, -1, 0], [1, 0, 0]])

 

Eigenvalues(P, G)

Vector(2, {(1) = (1/2)*beta+1/2+(1/2)*kappa+(1/2)*sqrt(beta^2-2*beta+2*kappa*beta+1+2*kappa+kappa^2), (2) = (1/2)*beta+1/2+(1/2)*kappa-(1/2)*sqrt(beta^2-2*beta+2*kappa*beta+1+2*kappa+kappa^2)})

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