### From Wikipedia

Canonical analysis, an integral part of the general linear model for the analysis of data, belongs to a family of methods which involve solving the characteristic equation for its latent roots and vectors. Canonical analysis describes formal structures in hyperspace, defined by orthogonal references axes and invariant with respect to rotation of their coordinates. In this type of solution, rotation leaves many optimizing properties preserved, provided it takes place in certain ways and in a subspace. This rotation from the maximum intervariate correlation structure into a different, simpler and more meaningful structure increases the interpretability of the obtained structures. In this the canonical analysis differs from the Hotellingâ€™s (1936) canonical variate analysis, designed to obtain the maximum (canonical) correlation between a set of predictor and a set of criterion canonical variates.

References

Cliff, N. and Krus, D. J. (1976) Interpretation of canonical analysis: Rotated vs. unrotated solutions. Psychometrika, 41, 1, 35-42.

Hotelling, H. (1936) Relations between two sets of variates. Biometrika, 28, 321-377

Krus, D.J., et al. (1976) Rotation in Canonical Analysis. Educational and Psychological Measurement, 36, 725-730.

Liang, K.H., Krus, D.J., & Webb, J.M. (1995) K-fold crossvalidation in canonical analysis. Multivariate Behavioral Research, 30, 539-545.