Sarrus' Quilt: A Novel Way to Compute Determinants

TL;DR

The paper introduces Sarrus' Quilt, a new visual method for computing determinants of 4x4 and larger matrices, revealing symmetric and cyclic patterns that simplify the calculation process.

Contribution

It presents a novel, pattern-based approach to determinant calculation for 4x4 and larger matrices, extending Sarrus' rule beyond 3x3.

Findings

Discovered a symmetric pattern for 4x4 determinants

Identified a cyclic pattern for larger determinants

Provided a shortcut method for determinant computation

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.