  In recent years, several algorithms, which approximate matrix decomposition,
have been developed. These algorithms are based on metric conservation features
for linear spaces of random projection types. We show that an i.i.d
sub-Gaussian matrix with large probability to have zero entries is metric
conserving. We also present a new algorithm, which achieves with high
probability, a rank $r$ decomposition approximation for an $m \times n$ matrix
that has an asymptotic complexity like state-of-the-art algorithms. We derive
an error bound that does not depend on the first $r$ singular values. Although
the proven error bound is not as tight as the state-of-the-art bound,
experiments show that the proposed algorithm is faster in practice, while
getting the same error rates as the state-of-the-art algorithms get.
