## Strictly Triangular Matrices

If the entries on the diagonal of an upper (or lower) triangular matrix are all 0, the matrix is said to be strictly upper (or lower) triangular.Example: The matrix

\[ \left| \begin{array}{ccc} 0 & 2 & 1 \\ 0 & 0 & 4 \\ 0 & 0 & 0 \end{array} \right| \]

is strictly upper triangular and the matrix \[ \left| \begin{array}{ccc} 0 & 0 & 0 \\ 2 & 0 & 0 \\ 3 & 0 & 0 \end{array} \right| \]

is strictly lower triangular.