View source for Non-derogatory matrix

An <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n120/n120090/n1200901.png" />-matrix <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n120/n120090/n1200902.png" /> such that for each of its distinct eigenvalues (cf. [[Eigen value|Eigen value]]; [[Matrix|Matrix]]) <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n120/n120090/n1200903.png" /> there is, in its [[Jordan normal form|Jordan normal form]], only one Jordan block with that eigenvalue. A matrix <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n120/n120090/n1200904.png" /> is non-derogatory if and only if its [[Characteristic polynomial|characteristic polynomial]] and minimum polynomial (cf. [[Minimal polynomial of a matrix|Minimal polynomial of a matrix]]) coincide (up to a factor <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n120/n120090/n1200905.png" />). A matrix that is not non-derogatory is said to derogatory.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J. Stoer,   R. Bulirsch,   "Introduction to numerical analysis" , Springer  (1993)  pp. 338ff</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  Ch.G. Cullen,   "Matrices and linear transformations" , Dover, reprint  (1990)  pp. 236ff</TD></TR></table>