[Math] Is the identity matrix an upper triangular matrix

Question

I know an upper triangular matrix is considered to be a matrix with 0 entries below the diagonal, but is the identity matrix considered to be a special case of an upper triangular matrix? Is it an upper triangular matrix?

Answer 1

Yes. Diagonal matrices are both upper and lower triangular.

Notice that the definition for upper triangular says that entries below the diagonal are all zero. It doesn't matter what the entries above the diagonal are.