\[\int_{\mathbf{O}(m)}Z_{\kappa}\left(\mathbf{S}\mathbf{H}\mathbf{T}\mathbf{H}^{%
-1}\right)\mathrm{d}{\mathbf{H}}=\frac{Z_{\kappa}\left(\mathbf{S}\right)Z_{%
\kappa}\left(\mathbf{T}\right)}{Z_{\kappa}\left(\mathbf{I}\right)}.\]