Conditional negativity of anti-Loewner matrices
Chikara Hidaka, Takashi Sano · Linear and Multilinear Algebra · 2011
Let f be a positive, continuously differentiable function on (0, ∞). We consider matrices K f of the form We show that for such a function f with f(0) = f ′(0) = 0, all K f are conditionally negative definite if and only if all are positive semidefinite (p.s.d.), and give the integral representation of f. We also study functions f with K f (·, ·) conditionally negative definite or p.s.d.