Non-derogatory matrix

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

An $(n\times m)$-matrix $A$ such that for each of its distinct eigenvalues (cf. Eigen value; Matrix) $\lambda$ there is, in its Jordan normal form, only one Jordan block with that eigenvalue. A matrix $A$ is non-derogatory if and only if its characteristic polynomial and minimum polynomial (cf. Minimal polynomial of a matrix) coincide (up to a factor $\pm1$). 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