Uper-triangular Matrix A square matrix A whose elements aij=0 for i>j is called upper triangular matrix.

No. Only square matrices can be triangular.

A strictly lower triangular matrix is a kind of (lower) triangular matrix.

Term "lower" implies matrix has elements only in the lower half. The condition "strictly" implies that even the "diagonal" of such lower triangular matrix is populated with '0's. The strictly lower triangular matrix thus has '0's in its diagonal as well as the upper triangle part.

In other words, a strictly lower triangular matrix is a lower triangular matrix minus its diagonal.

Lower-triangular Matrix A square matrix A whose elements aij=0 for i

Diagonal Matrix A square matrix A which is both uper-triangular and lower triangular is called a diagonal matrix. Diagonal matrix is denoted by D.