The diagonal entries themselves may or may not be zero.

The diagonal entries of this matrix are the eigenvalues of A.

Prerequisite: The diagonal entries of the table are 0.

One can also take the diagonal entries of L to be positive.

This works because the diagonal entries are also the eigenvalues of this matrix.

We can always choose a D with positive diagonal entries.

L-matrices have the additional property that all diagonal entries are greater than zero.

Moreover its diagonal entries all equal 1, so it has determinant 1.

The lower triangular matrix with strictly positive diagonal entries is invertible.

The condition of divisibility of diagonal entries might not be satisfied.