Abstract
By applying the canonical correlation decomposition of matrix pairs, the general fixed rank least square solutions of matrix equation Xβ=Y are derived. As statistical applications, an algorithm for computing the least square estimator of the multivariate reduced rank regression model Y=Xβ+ϵ, r(β)=t is given.
Acknowledgements
This work was supported by the Foundation of Shanghai Education Committee (07zz171). The author is grateful for the detailed comments from an anonymous referee.