>[!summary] A triangular matrix is a square matrix where entries above or below the main diagonal are 0. >[!info]+ Read Time **⏱ 1 min** # Definition A triangular matrix is a [[Square Matrix|square matrix]] where all entries either above or below the main [[Diagonal Matrix|diagonal]] are 0. An upper triangle, all entries below the diagonal are 0, while a lower triangle, all entries above the diagonal are 0. Formally generalized for $\mathbb{R}^n$ below. $ \begin{array}{c} \text{Upper Triangle}: \\ \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ 0 & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & a_{nn} \end{bmatrix} \\ \\ \text{Lower Triangle}: \\ \begin{bmatrix} a_{11} & 0 & \cdots & 0 \\ a_{21} & a_{22} & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & \cdots & a_{nn} \end{bmatrix} \end{array} $