Bruno Codenotti, Pavel Pudlak, Giovanni Resta

We consider the conjecture stating that a matrix with rank

$o(n)$ and ones on the main diagonal must contain nonzero

entries on a $2\times 2$ submatrix with one entry on the main

diagonal. We show that a slightly stronger conjecture implies

that ...
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Mrinal Kumar, Ben Lee Volk

We study the problem of constructing explicit families of matrices which cannot be expressed as a product of a few sparse matrices. In addition to being a natural mathematical question on its own, this problem appears in various incarnations in computer science; the most significant being in the context of ... more >>>

Mrinal Kumar, Ben Lee Volk

We show that there is a defining equation of degree at most poly(n) for the (Zariski closure of the) set of the non-rigid matrices: that is, we show that for every large enough field $\mathbb{F}$, there is a non-zero $n^2$-variate polynomial $P \in \mathbb{F}(x_{1, 1}, \ldots, x_{n, n})$ of degree ... more >>>