  The most general homogeneous and isotropic statistical ensemble of linear
scalar perturbations which are regular at early times, in a universe with only
photons, baryons, neutrinos, and a cold dark matter (CDM) component, is
described by a 5x5 symmetric matrix-valued generalization of the power
spectrum. This description is complete if the perturbations are Gaussian, and
even in the non-Gaussian case describes all observables quadratic in the small
perturbations. The matrix valued power spectrum describes the auto- and
cross-correlations of the adiabatic, baryon isocurvature, CDM isocurvature,
neutrino density isocurvature, and neutrino velocity isocurvature modes. In
this paper we examine the prospects for constraining or discovering
isocurvature modes using forthcoming MAP and PLANCK measurements of the cosmic
microwave background (CMB) anisotropy. We also consider the degradation in
estimates of the cosmological parameters resulting from the inclusion of these
modes. In the case of MAP measurements of the temperature alone, the
degradation is drastic. When isocurvature modes are admitted, uncertainties in
the amplitudes of the mode auto-- and cross--correlations, and in the
cosmological parameters, become of order one. With the inclusion of
polarisation (at an optimistic sensitivity) the situation improves for the
cosmological parameters but the isocurvature modes are still only weakly
constrained. Measurements with PLANCK's estimated errors are far more
constraining, especially so with the inclusion of polarisation. If PLANCK
operates as planned the amplitudes of isocurvature modes will be constrained to
less than ten per cent of the adiabatic mode and simultaneously key
cosmological parameters will be estimated to a few per cent or better.
