Difference between revisions of "Non-derogatory matrix"
From Encyclopedia of Mathematics
(MSC 15A18) |
(reword) |
||
| Line 1: | Line 1: | ||
{{TEX|done}}{{MSC|15A18}} | {{TEX|done}}{{MSC|15A18}} | ||
| − | An $ | + | An square [[matrix]] $A$ for which the [[characteristic polynomial]] and [[Minimal polynomial of a matrix|minimal polynomial]] coincide (up to a factor $\pm1$). Equivalently, for each of its distinct [[Eigen value|eigenvalue]]s $\lambda$ there is, in the [[Jordan normal form]] for $A$, only one Jordan block with that eigenvalue $\lambda$. A matrix that is not non-derogatory is said to derogatory. |
====References==== | ====References==== | ||
Revision as of 18:18, 22 November 2016
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 $\lambda$. 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=39804
Non-derogatory matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-derogatory_matrix&oldid=39804
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article