2
votes
1answer
184 views

Multiple eigenvalues over imperfect fields

Let $K$ be a field. For a matrix $A\in GL_n(K)$ we can find the Jordan normal form $A'$ in $GL_n(\overline{K})$, where $\overline{K}$ is the algebraic closure of $K$. We write $j_\alpha(A)$ for the ...
3
votes
2answers
324 views

Rank of sum of Galois conjugates of a matrix

Given an invertible square matrix $M$ with entries from some number field $K$ which is Galois over $\mathbb{Q}$, sum the Galois conjugates of $M$ to form a new matrix $M' = \Sigma_{\sigma \in ...
12
votes
3answers
848 views

“Conjugacy rank” of two matrices over field extension

EDIT: ARGH! I've got to go and I have no idea how to do the damn subscripts right. I have posted this elsewhere and got only a partial reply. I don't know whether this qualifies the question for an ...