Non-Asymptotic Theory of Random Matrices
نویسندگان
چکیده
Let A be an n × n subgaussian matrix (entries are i.i.d. subgaussian r.v’s with variance 1). There are two reasons for the invertibility of A, depending on the nature of the unit vector on which A is acting – either compressible or incompressible. We recall that compressible vectors are those whose distance is at most some constant ρ from the set of (δn)-sparse vectors, and incompressible vectors are those that are not compressible. It is obvious that the unit sphere Sn−1 is the disjoint union of the compressible vectors (Comp) and the incompressible vectors (Incomp). We have the following lemmas for A Gaussian.
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