Canonical correlations and canonical variates

In this chapter we shall summarize the essential elements of the theory of canonical correlations and variates. We shall begin by formulating the problem. The derivation of canonical correlations and canonical variates will then be taken up. Canonical analysis can be derived in several ways. Two derivations will be described rather fully — those leading to eigenanalysis and singular value decomposition, respectively. Several other derivations are of interest for the light which they shed on canonical analysis and its relations with other methods, and these will be described more briefly. We shall then consider the properties of canonical correlations, weights and variates. Finally, computational aspects of canonical analysis will be taken up.