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- W2035168057 abstract "Lett≥1 and letn, M be natural numbers,n<M. Leta=(a i,j ) be ann xM matrix whose rows are orthonormal. Suppose that the ℓ2-norms of the columns ofA are uniformly bounded. Namely, for allj $$sqrt {frac{M}{n}} cdot left( {sumlimits_{i = 1}^n {a_{i,j}^2 } } right)^{1/2} leqslant t.$$ Using majorizing measure estimates we prove that for every ε>0 there exists, a setI ⊃ {1,…,M} of cardinality at most $$C cdot frac{{t^2 }}{{varepsilon ^2 }} cdot n cdot logfrac{{nt^2 }}{{varepsilon ^2 }}$$ such that the matrix $$sqrt {M/left| I right|} cdot A_I^T $$ , whereA I =(a i,j ) j∈I , acts as a (1+ε)-isomorphism from ℓ 2 into $$ell _2^{backslash Ibackslash } $$ ." @default.
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- W2035168057 date "1999-12-01" @default.
- W2035168057 modified "2023-09-27" @default.
- W2035168057 title "Almost orthogonal submatrices of an orthogonal matrix" @default.
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- W2035168057 doi "https://doi.org/10.1007/bf02810682" @default.
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