A generalized eigenvalue is a ratio = / such that AX = BX or

det(A-B) = 0 for general matrices A, B, and X. is typically represented as a ratio rather than as a scalar because there are reasonable interpretations for = 0, = 0, and for = = 0. A right generalized eigenvector x corresponding to a generalized eigenvalue is defined by (A - B)x = 0. A left generalized eigenvector x corresponding to a generalized eigenvalue is defined by

(A - B)Hx = 0. A good reference for generalized eigenproblems is the book *Matrix Computations*, 2nd. ed. by Golub and van Loan (1989, The Johns Hopkins University Press).