11. But then must be diagonal, for, as noted above, a normal upper-triangular matrix is diagonal. 12. For example, a real triangular matrix has its eigenvalues along its diagonal, but in general is not symmetric. 13. The factorization is stored as a lower triangular matrix , with the elements in the upper triangle set to zero. 14. The application of the Gram Schmidt process to the column vectors of a full column orthogonal and a triangular matrix ). 15. The Crout algorithm is slightly different and constructs a lower triangular matrix and a " unit upper triangular " matrix. 16. The determinant of the ( upper ) triangular matrix " D " is the product of its entries on the main diagonal :. 17. Using these operations, a matrix can always be transformed into an upper triangular matrix , and in fact one that is in row echelon form. 18. The LU decomposition factorizes a matrix into a lower triangular matrix " L " and an upper triangular matrix " U ". 19. The LU decomposition factorizes a matrix into a lower triangular matrix " L " and an upper triangular matrix " U ". 20. We transform the matrix " A " into an upper triangular matrix " U " by eliminating the entries below the main diagonal.
