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ℓ_p-Spread and Restricted Isometry Properties of Sparse Random Matrices
[article]

2022
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arXiv
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pre-print

Random subspaces X of ℝ^n of dimension proportional to n are, with high probability, well-spread with respect to the ℓ_2-norm. Namely, every nonzero x ∈ X is "robustly non-sparse" in the following sense: x is εx_2-far in ℓ_2-distance from all δ n-sparse vectors, for positive constants ε, δ bounded away from 0. This "ℓ_2-spread" property is the natural counterpart, for subspaces over the reals, of the minimum distance of linear codes over finite fields, and corresponds to X being a Euclidean

arXiv:2108.13578v2
fatcat:rg5xhaa3xzbghiogjrarebgl4m