Quantitative estimates of the spectral norm of random matrices with independent columns

2023/07/06 by Dai, Guozheng, Su, Zhonggen, Wang, Hanchao
#46B09 #46B20 #60E15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2307.03069

Abstract

This paper investigates the nonasymptotic properties of the spectral norm of some random matrices with independent columns. In particular, we consider an m× n random matrix BA, where A is an N× n random matrix with independent mean-zero subexponential entries, and B is an m× N deterministic matrix. We prove that the L_p norm of the spectral norm of BA is upper bounded by (√(m)+√(n))p. It is remarkable that this result is independent of the dimension N.

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