  A recent breakthrough by Tang (STOC 2019) showed how to "dequantize" the
quantum algorithm for recommendation systems by Kerenidis and Prakash (ITCS
2017). The resulting algorithm, classical but "quantum-inspired", efficiently
computes a low-rank approximation of the users' preference matrix. Subsequent
works have shown how to construct efficient quantum-inspired algorithms for
approximating the pseudo-inverse of a low-rank matrix as well, which can be
used to (approximately) solve low-rank linear systems of equations. In the
present paper, we pursue this line of research and develop quantum-inspired
algorithms for a large class of matrix transformations that are defined via the
singular value decomposition of the matrix. In particular, we obtain classical
algorithms with complexity polynomially related (in most parameters) to the
complexity of the best quantum algorithms for singular value transformation
recently developed by Chakraborty, Gily\'{e}n and Jeffery (ICALP 2019) and
Gily\'{e}n, Su, Low and Wiebe (STOC19).
