In order to achieve in-memory photonic multiplication, we first send an optical pulse down a wave guide to set the state of the GST. This changes the transmission of the GST in an unvolatile manner so that we can encode a number between 0 and 1, which we will call A. Next we send a second optical pulse, which is at a much lower power. This encodes the second number B, which we wish to multiply with A. Finally, we measure the output power on a photodetector, which is the multiplication of both A and B. Since the state of the GST does not change, we can multiply as many numbers as we want at the speed of light by multiplying different amplitudes of B with the constant value of A. So if we combine two of these unit cells in parallel, we can achieve basic matrix vector multiplication. On the left we have our original unit cell, where we are multiplying A, which is encoded in the GST transmission, and B, which is encoded in the optical pulse amplitude. On the other side we have an additional unit cell, where we have encoded the number C in the GST and D in the optical pulse. Since these two waveguides combine, we have the addition of A times B plus C times D, which outputs to a photodetector. This will give us the result of a two element matrix vector multiplication.