Talk:Companion matrix

Companion matrix or companion morphism?

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)

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)

Time varying coefficients in ODE section

In the ODE section it is mentioned that the coefficients c_i may be time-varying, however immediately after coordinate transformations are discussed. However if c_i are time-dependent, then these coordinate transformation in general also have to be time-dependent and derivatives of these transformation enter the picture and I doubt that all statements are still true then. My suggestion would be to just remove this sentence. ~2026-47831-24 (talk) 07:45, 3 September 2026 (UTC)