Talk:Companion matrix

Companion matrix or companion morphism?[edit]

In the article the companion matrix is defined as a function on the space of polynomials

C:K_{n}[x]\rightarrow K^{n\,\times \,n}

without any mention of it. So, for sake of simplicity I suggest to drop the $C (p)$ notation in favor of $C p$ . Further, it could be interesting to extend the section on Diagonalizability to study the effects the change of base in $K n [x]$ as well. 213.55.225.91 (talk) 10:17, 12 March 2023 (UTC)[reply]

One could add a sentence that says the above, that C is a function from the polynomial ring to the general linear group, but doing so would implicitly suggest that this map is perhaps a homomorphism of some kind. But it isn't. If you multiply two polynomials, you don't get a product of the matrices. The polynomial ring has a grading, the general linear group doesn't. Stuff like that. But I dunno, maybe I'm missing something basic. 67.198.37.16 (talk) 03:32, 15 January 2024 (UTC)[reply]