Triangular matrix

Summary

A triangular matrix is a square matrix that is either upper triangular or lower triangular. All its entries on one side of the main diagonal are zero. Linear systems with a triangular matrix are solved quickly by substitution. The determinant of a triangular matrix is the product of its diagonal entries, and these entries are its eigenvalues. Many factorisations, such as LU, QR and the Schur decomposition, produce triangular factors.