Can a Triangular Matrix Have Zero on the Diagonal?

An upper triangular matrix whose diagonal consists of nothing but zeros is called strictly upper triangular. The above matrix is an example of a strictly upper triangular matrix. Similarly, any lower triangular matrix with zero diagonal is called strictly lower triangular.

Can a diagonal matrix have a zero on the diagonal?

2.6.

A diagonal matrix is defined as a square matrix in which all off-diagonal entries are zero. (Note that a diagonal matrix is necessarily symmetric.) Entries on the main diagonal may or may not be zero. If all entries on the main diagonal are equal scalars, then the diagonal matrix is called a scalar matrix.

Can diagonal elements be zero in a triangular matrix?

A matrix with all elements under/above the main diagonal equal to zero is called an upper/lower triangular matrix. ... Determinant of upper or lower triangular matrix is equal to the product of its diagonal elements.