A method for real-time matrix multiplication is presented. This paper describes the geometrical interpretation of the mathematical manipulations between the two matrices. Three coherent optical astigmatic systems are developed based on the analysis. Each system is essentially composed of two subsystems that are connected in series. The first one performs multiplications between the corresponding elements of the matrices coded in the amplitude transmittance of the transparencies. The results are received by the second subsystem that performs the necessary summation operations to give the calculated rise to each element in the final result, the product of the two matrices. In these processes, no preparation of a hologram or intermediate memory is required. The operations are done in parallel. The multiplication between an N x N matrix and an N x 1 vector is discussed in detail. Multiplication between N x N and N x N matrices is also presented.