Dimension expanders

We show that there exists and such that for every field F of characteristic zero and for every , there exist explicitly given linear transformations satisfying the following: For every subspace W of Fn of dimension less or equal , . This answers a question of Avi Wigderson [A. Wigderson, A lecture at IPAM, UCLA, February 2004]. The case of fields of positive characteristic (and in particular finite fields) is left open.