Systems and methods for performing signed matrix operations using a linear photonic processor are provided. The linear photonic processor is formed as an array of first amplitude modulators and second amplitude modulators, the first amplitude modulators configured to encode elements of a vector into first optical signals and the second amplitude modulators configured to encode a product between the vector elements and matrix elements into second optical signals. An apparatus may be used to implement a signed value of an output of the linear processor. The linear photonic processor may be configured to perform matrix-vector and/or matrix-matrix operations.