Relations between quark and lepton mixing angles and matrices

We discuss the relations between the mixing angles and the mixing matrices of quarks and leptons. With Raidal’s numerical relations, we parametrize the lepton mixing (PMNS) matrix with the parameters of the quark mixing (CKM) matrix, and calculate the products of $V_{\mathrm{C}\mathrm{K}\mathrm{M}}{U}_{\mathrm{P}\mathrm{M}\mathrm{N}\mathrm{S}}$ and $U_{\mathrm{P}\mathrm{M}\mathrm{N}\mathrm{S}}{V}_{\mathrm{C}\mathrm{K}\mathrm{M}}$. Also, under the conjectures $V_{\mathrm{C}\mathrm{K}\mathrm{M}}{U}_{\mathrm{P}\mathrm{M}\mathrm{N}\mathrm{S}}=U_{\mathrm{b}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{x}}$ or $U_{\mathrm{P}\mathrm{M}\mathrm{N}\mathrm{S}}{V}_{\mathrm{C}\mathrm{K}\mathrm{M}}=U_{\mathrm{b}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{x}}$, we get the PMNS matrix naturally, and test Raidal’s relations in these two different versions. The similarities and the differences between the different versions are discussed in detail.