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Non-derogatory matrix

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2010 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://www.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