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