91Ó°ÊÓ

An upper triangular matrix is a square matrix with all elements below the main diagonal being zero, e.g., \[ \begin{bmatrix} 4 & 3 & 2 \\ 0 & 1 & 5 \\ 0 & 0 & 6 \end{bmatrix} \] A lower triangular matrix is a square matrix with all elements above the main diagonal being zero, e.g., \[ \begin{bmatrix} 7 & 0 & 0 \\ 8 & 3 & 0 \\ 1 & 6 & 9 \end{bmatrix} \] A properly triangular matrix is a triangular matrix where all main diagonal elements are also zero, e.g., upper properly triangular matrix: \[ \begin{bmatrix} 0 & 5 & 4 \\ 0 & 0 & 8 \\ 0 & 0 & 0 \end{bmatrix} \] and lower properly triangular matrix: \[ \begin{bmatrix} 0 & 0 & 0 \\ 4 & 0 & 0 \\ 9 & 2 & 0 \end{bmatrix} \]