# Non-derogatory matrix

From Encyclopedia of Mathematics

2020 Mathematics Subject Classification: *Primary:* 15A18 [MSN][ZBL]

An square matrix $A$ for which the characteristic polynomial and minimal polynomial coincide (up to a factor $\pm1$). Equivalently, for each of its distinct eigenvalues $\lambda$ there is, in the Jordan normal form for $A$, only one Jordan block with that eigenvalue $\lambda$; this is in turn equivalent to each distinct eigenvalue having only one independent eigenvector, that is, geometric multiplicity one.

A **derogatory matrix** is one that is not non-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=39806

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