Non-derogatory matrix

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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
How to Cite This Entry:
Non-derogatory matrix. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article