On singular values of matrices with independent rows

Shahar Mendelson; Alain Pajor

doi:10.3150/bj/1161614945

On singular values of matrices with independent rows

Shahar Mendelson
, Alain Pajor

Research output: Contribution to journal › Article › peer-review

36 Citations (Scopus)

Abstract

We present deviation inequalities of random operators of the form N^-1 Σ^N _i=1 X_i ⨂ X_i from the average operator 𝔼(X ⨂ X), where Xi are independent random vectors distributed as X, which is a random vector in ℝⁿ or in ℒ₂. We use these inequalities to estimate the singular values of random matrices with independent rows (without assuming that the entries are independent).

Original language	English
Pages (from-to)	761-773
Number of pages	13
Journal	Bernoulli
Volume	12
Issue number	5
DOIs	https://doi.org/10.3150/bj/1161614945
Publication status	Published - 1 Jan 2006

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abstract = "We present deviation inequalities of random operators of the form N-1 ΣN i=1 Xi ⨂ Xi from the average operator 𝔼(X ⨂ X), where Xi are independent random vectors distributed as X, which is a random vector in ℝn or in ℒ2. We use these inequalities to estimate the singular values of random matrices with independent rows (without assuming that the entries are independent).",

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N2 - We present deviation inequalities of random operators of the form N-1 ΣN i=1 Xi ⨂ Xi from the average operator 𝔼(X ⨂ X), where Xi are independent random vectors distributed as X, which is a random vector in ℝn or in ℒ2. We use these inequalities to estimate the singular values of random matrices with independent rows (without assuming that the entries are independent).

AB - We present deviation inequalities of random operators of the form N-1 ΣN i=1 Xi ⨂ Xi from the average operator 𝔼(X ⨂ X), where Xi are independent random vectors distributed as X, which is a random vector in ℝn or in ℒ2. We use these inequalities to estimate the singular values of random matrices with independent rows (without assuming that the entries are independent).

KW - Random vectors in ℝ

KW - Singular values of integral operators

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DO - 10.3150/bj/1161614945

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EP - 773

JO - Bernoulli

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On singular values of matrices with independent rows

Abstract

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