An invariance property of Hankel forms (Q1824667)

Let k be an arbitrary field, x a variable, k(x) a function field, \(y\in g(x)/h(x)\in k(x),\) \(n=[k(x):k(y)].\) The authors introduce a nondegenerate bilinear form \(H_{xy}\) which they call Hankel form. They show, if \(x'=\lambda (x)\) and \(y'=\mu (y),\) where \(\lambda,\mu \in PGL_ 2(k)\), then \[ H_{x'y'}\simeq \det \lambda \cdot \det \mu \cdot H_{xy}. \]