Special Matrices

6. A lower triangular matrix is a square matrix that has $0$s anywhere above the main diagonal.
   • The elements on the diagonal and below it could be anything, including any $0$s.
   • We could use the letter $L$ to denote a lower triangular matrix.
     • For the lower triangular matrix $L_n = [l_{i,j}]$, we have $l_{i,j} = 0$, where $1 \le i, j \le n$ and $i < j$.
   • A diagonal matrix is a specific case of a lower triangular matrix, too.
   Examples:

   21. $E_1 = \begin{bmatrix} 🗽 \end{bmatrix}$

   29. $L_2 = \begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix}$

   30. $L_3 = \begin{bmatrix} a & 0 & 0 \\ b & c & 0 \\ d & e & f \end{bmatrix}$

   31. $L_4 = \begin{bmatrix} \log 5 & 0 & 0 & 0 \\ 7 & 1.11 & 0 & 0 \\ 0 & \frac{1}{2} & 2^{100} & 0 \\ 0.4 & 9e2 & 0 & 1\end{bmatrix}$