# Non-derogatory matrix

From Encyclopedia of Mathematics

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.

#### References

[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: http://encyclopediaofmath.org/index.php?title=Non-derogatory_matrix&oldid=18949

This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article