On the conjugacy classes in the orthogonal and symplectic groups over algebraically closed fields

Let F$\mathbb{F}$ be an algebraically closed field. Let V$\mathbb{V}$ be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form B   over F$\mathbb{F}$. Suppose the characteristic of F$\mathbb{F}$ is sufficiently large  , i.e. either zero or greater than the dimension of V$\mathbb{V}$. Let I(V,B)$I(\mathbb{V},\mathbb{B})$ denote the group of isometries. Using the Jacobson–Morozov lemma we give a new and simple proof of the fact that two elements in I(V,B)$I(\mathbb{V},\mathbb{B})$ are conjugate if and only if they have the same elementary divisors.     

Characterization of full rank ACI-matrices over fields

An ACI-matrix over a field F$\mathbb{F}$ is a matrix whose entries are polynomials with coefficients on F$\mathbb{F}$, the degree of these polynomials is at most one in a number of indeterminates, and where no indeterminate appears in two different columns. In 2011 Huang and Zhan characterized the m×n$m\times n$ ACI-matrices such that all its completions have rank equal to min{m,n}$\min \{m,n\}$ whenever |F|?max{m,n+1}$|\mathbb{F}|?\max \{m,n+1\}$. We will give a characterization for arbitrary fields by introducing two classes of ACI-matrices: the maximal and the minimal full rank ACI-matrices.