Definition:Triangular Matrix/Upper Triangular Matrix

Definition
An upper triangular matrix is a matrix in which all the lower triangular elements are zero.

That is, all the non-zero elements are on the main diagonal or in the upper triangle.

That is, $\mathbf U$ is upper triangular :
 * $\forall a_{ij} \in \mathbf U: i > j \implies a_{ij} = 0$

Also defined as
Some sources define an upper triangular matrix only as a square matrix.

Also see

 * Definition:Lower Triangular Matrix