An -matrix such that for each of its distinct eigenvalues (cf. Eigen value; Matrix) there is, in its Jordan normal form, only one Jordan block with that eigenvalue. A matrix is non-derogatory if and only if its characteristic polynomial and minimum polynomial (cf. Minimal polynomial of a matrix) coincide (up to a factor ). A matrix that is not non-derogatory is said to derogatory.
|[a1]||J. Stoer, R. Bulirsch, "Introduction to numerical analysis" , Springer (1993) pp. 338ff|
|[a2]||Ch.G. Cullen, "Matrices and linear transformations" , Dover, reprint (1990) pp. 236ff|
Non-derogatory matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-derogatory_matrix&oldid=18949