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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

15 votes
Accepted

Endomorphisms of the p-adic group $(\mathbb Z_p,+)$

I claim that any endomorphism of $\mathbb{Z}_p$ is just multiplication by a constant. Let $f$ be an endomorphism of $\mathbb{Z}_p$. First observe that $p^n f(x) = f(p^n x)$, so $f$ takes $p^n \mathbb …
Dongryul Kim's user avatar
  • 1,474
10 votes
Accepted

Deceptive linear algebra problem

Let $$f(X) = (X - a_1) \cdots (X - a_p) = X^p + e_1 X^{p-1} + \dots + e_p.$$ Using $f(a_i) = 0$ for each $i$, we get \begin{equation} \begin{bmatrix} d_{p+1} & d_p & \cdots & d_1 \\ d_{p+2} & d_{p+1} …
Dongryul Kim's user avatar
  • 1,474