0
votes
0answers
206 views

Finding the effective maximum number of subspaces in a finite dimensional vector space

Hi mathoverflow community, may be some one may give me a hint on the following problem before I spend much time on brute force search. For $q$ a prime number and $n=6$, let $\mathbb {F}_{q}^{n}$ be ...
2
votes
1answer
269 views

nth-powers and degree n polynomials with coefficients in field extensions

Hi, Suppose that $E/F$ is a Galois extension. If $P(X)\in E[X]$ is a (EDIT: monic) polynomial of degree $n > 0$, such that $P(X)^n\in F[X]$, does it follow that $P(X)\in F[X]$? Thanks
8
votes
2answers
501 views

Field extension containing the eigenvectors of a Hermitian matrix

Let H be a (finite-dimensional) Hermitian matrix with algebraic numbers for its entries, all of which lie in some minimal field extension of the rational numbers; call this field ℚ(H) for short. ...
12
votes
3answers
847 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 ...