  Optics is a promising platform in which to help realise the next generation
of fast, parallel and energy-efficient computation. We demonstrate a
reconfigurable free-space optical multiplier that is capable of over 3000
computations in parallel, using spatial light modulators with a pixel
resolution of only 340x340. This enables vector-matrix multiplication and
parallel vector-vector multiplication with vector size of up to 56. Our design
is the first to simultaneously support optical implementation of
reconfigurable, large-size and real-valued linear algebraic operations. Such an
optical multiplier can serve as a building block of special-purpose optical
processors such as optical neural networks and optical Ising machines.
