A systolic array for Cholesky decomposition of an N×N matrix is described. A plurality of processing cells, including a corner cell, N−1 boundary cells, and (N2−3N+2)/2 internal cells, are arranged into N−1 rows and N columns of processing cells. Each row of processing cells is configured to calculate elements of a respective column of a lower triangular output matrix. Each processing cell of each row is configured to determine a value of a respective element of the lower triangular output matrix using a value of an element calculated in a previous processing cell of the row.