Name for a matrix similar to a companion matrix? Translating "Monogène" matrix from French I am currently translating a research paper from French (which I do not speak well). I have made good progress with copious use of google translate & switching between French & English versions of articles on wikipedia, coupled with knowledge in the given field. However, I am stuck on the following ($M$ is a matrix): ![enter image description here]( The parenthetical implies that $M$ is similar to a Companion Matrix, but I am stumped when it comes to what "monogène" means. Google translate says "monogenic", which I would infer to be the author's term for "similar to the companion matrix of a polynomial." However, I can't say that I've come across the term "Monogenic Matrix" before, plus this would just be the Froebius normal form / rational canonical form of a matrix with only one block. Is this a reasonable translation/interpretation?

Such a matrix is said to be _non-derogatory_ in English. The condition is equivalent to one of

* having equal minimal and characteristic polynomials,

* having a cyclic vector,

* being similar to a companion matrix.