  The principal component analysis of flow correlations in heavy-ion collisions
is studied. The correlation matrix of harmonic flow is generalized to
correlations involving several different flow vectors. The method can be
applied to study the nonlinear coupling between different harmonic modes in a
double differential way in transverse momentum or pseudorapidity. The procedure
is illustrated with results from the hydrodynamic model applied to Pb+Pb
collisions at $\sqrt{s}=2760$GeV. Three examples of generalized correlations
matrices in transverse momentum are constructed corresponding to the coupling
of $v_2^2$ and $v_4$, of $v_2v_3$ and $v_5$, or of $v_2^3$, $v_3^3$, and $v_6$.
The principal component decomposition is applied to the correlation matrices
and the dominant modes are calculated.
