Sarrus' Quilt: A Novel Way to Compute Determinants

Abstract

After analyzing the 4x4 determinant of a matrix, a shortcut was obtained to find such a determinant. Similarly to the Sarrus method for 2x2 or 3x3 determinants, the method consists of laying 19 columns of size 4 each and adding and subtracting some diagonal multiplications. There is a symmetry in the arrangement of these columns. A very symmetric pattern emerged for the 5x5 determinant which was also found. A cyclic pattern was observed for the diagonals of larger determinants when applying this method.