If \(\Psi (|z|) \ge 0\), then the Landau matrix \(A(z)\) is positive semi-definite: \(Y^T A(z) Y \ge 0\) for all \(Y \in \mathbb {R}^3\).

If \(\Psi (|z|) {\gt} 0\) and \(z \ne 0\), then \(Y^T A(z) Y = 0\) iff \(Y \parallel z\).