Equivalence testing for a polynomial family $\{g_m\}_{m \in \mathbb{N}}$ over a field F is the following problem: Given black-box access to an $n$-variate polynomial $f(\mathbb{x})$, where $n$ is the number of variables in $g_m$ for some $m \in \mathbb{N}$, check if there exists an $A \in \text{GL}(n,\text{F})$ such that $f(\mathbb{x}) ... more >>>

Let us call a matrix $X$ as a linear matrix if its entries are affine forms, i.e. degree one polynomials. What is a minimal-sized representation of a given matrix $F$ as a product of linear matrices? Finding such a minimal representation is closely related to finding an optimal way to ... more >>>