  Redshift evolution and peculiar velocities break the isotropy of cosmological
surveys with respect to the directions parallel and transverse to the line of
sight, limiting the accuracy of the Fourier representation to small areas and
redshift ranges. In contrast to the Fourier space power spectrum, the full
information about the two-point function of tracers of large-scale structure is
encapsulated in the redshift-dependent angular power spectrum $C_\ell^{ij}
(z_i,z_j)$ for the tracer species $i$ and $j$ at the redshift slices $z_i$ and
$z_j$, expressed in harmonic space. In this paper we derive semi-analytical
expressions for the multi-tracer Fisher matrix of angular power spectra, in
real and in redshift space, which are exact in the linear regime of structure
formation. Our expressions can be used to forecast the constraining power of
galaxy surveys with many tracers and a large number of redshift slices, for
which the derivation of the Fisher matrix from numerically evaluated covariance
matrices may not be feasible or practical.
