Talk:Companion matrix
Latest comment: 3 months ago by 67.198.37.16 in topic Companion matrix or companion morphism?
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Companion matrix or companion morphism? edit
In the article the companion matrix is defined as a function on the space of polynomials
![{\displaystyle C:K_{n}[x]\rightarrow K^{n\,\times \,n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26f88b377595749911ed3c3e3cfdf497d2539e40)
without any mention of it. So, for sake of simplicity I suggest to drop the C(p) notation in favor of Cp. Further, it could be interesting to extend the section on Diagonalizability to study the effects the change of base in Kn[x] as well. 213.55.225.91 (talk) 10:17, 12 March 2023 (UTC)
- 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)