Eigenvectors of real and complex matrices byLR andQR triangularizations

In a recent paper [4] the triangularization of complex Hessenberg matrices using the LR algorithm was described. Denoting the Hessenberg matrix by H and the final triangular matrix by T we have $${P^{ - 1}}HP = T$$ (1) , where P is the product of all the transformation matrices used in the execution of the LR algorithm. In practice H will almost invariably have been derived from a general complex matrix A using the procedure comhes [3] and hence for some nonsingular S we have $${P^{ - 1}}{S^{ - 1}}ASP = T$$ (2) .