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The singular value decomposition (SVD) and the principal component analysisare fundamental tools and probably the most popular methods for data dimensionreduction. The rapid growth in the size of data matrices has lead to a need fordeveloping efficient large-scale SVD algorithms. Randomized SVD was proposed,and its potential was demonstrated for computing a low-rank SVD (Rokhlin etal., 2009). In this article, we provide a consistency theorem for therandomized SVD algorithm and a numerical example to show how the randomprojections to low dimension affect the consistency.

A Consistency Theorem for Randomized Singular Value Decomposition