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.
|[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|
Non-derogatory matrix. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Non-derogatory_matrix&oldid=39806