Triangular matrices

An matrix $ L$ is called a lower triangular matrix if all the ``entries above the diagonal'' are zeros, and an matrix $ U$ is called an upper triangular matrix if all the ``entries below the diagonal'' are zeros. For example,

$\displaystyle L = \begin{bmatrix}
1 & 0 & 0 & 0 \\
2 & -3 & 0 & 0 \\
1 & 4 & 2 & 0 \\
-1 & 1 & 3 & 1
\end{bmatrix}$    and $\displaystyle \quad
U = \begin{bmatrix}
4 & -1 & 3 & 2 \\
0 & 2 & 1 & -5 \\
0 & 0 & -1 & 9 \\
0 & 0 & 0 & 7
\end{bmatrix}$



Department of Mathematics
Last modified: 2005-10-21