  Traditionally, batch least squares (BLS) and recursive least squares (RLS)
are used for identification of a vector of parameters that form a linear model.
In some situations, however, it is of interest to identify parameters in a
matrix structure. In this case, a common approach is to transform the problem
into standard vector form using the vectorization (vec) operator and the
Kronecker product, known as vec-permutation. However, the use of the Kronecker
product introduces extraneous zero terms in the regressor, resulting in
unnecessary additional computational and space requirements. This work derives
matrix BLS and RLS formulations which, under mild assumptions, minimize the
same cost as the vec-permutation approach. This new approach requires less
computational complexity and space complexity than vec-permutation in both BLS
and RLS identification. It is also shown that persistent excitation guarantees
convergence to the true matrix parameters. This method can used to improve
computation time in the online identification of multiple-input,
multiple-output systems for indirect adaptive model predictive control.
