Dimension expanders
Abstract
We show that there exists k ∈ and 0 < ∈ such that for every field F of characteristic zero and for every n ∈ , there exists explicitly given linear transformations T1,..., Tk: Fn Fn satisfying the following: For every subspace W of Fn of dimension less or equal n2, (W+Σlki=1 TiW) (1+) W. This answers a question of Avi Wigderson [W]. The case of fields of positive characteristic (and in particular finite fields) is left open.
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