Special purpose integrated circuits and methods for matrix multiplication are disclosed. In some embodiments, a special purpose integrated circuit is constructed to perform mathematical operations. For matrix A and matrix B, an outer product of each column i of matrix A [vector Ai] and a corresponding row i of matrix B [vector Bi], for all i, is used to calculate all the products used for determining matrices A and B. A product matrix C (where A×B=C) is assembled using additions of the elements of the calculated outer products. Each outer product of Ai and Bi may be calculated using a series of vector-scalar products. Each vector-scalar product is calculated using the vector Bi and a selected element of Ai as the scalar. Thus, calculating the vector-scalar product for all the elements of Ai will produce the outer product of Ai and Bi.