  Based on the property that solving the system of linear matrix equations via
the column space and the row space projections boils down to an approximation
in the least squares error sense, a formulation for learning the weight
matrices of the multilayer network can be derived. By exploiting into the vast
number of feasible solutions of these interdependent weight matrices, the
learning can be performed analytically layer by layer without needing of
gradient computation after an initialization. Possible initialization schemes
include utilizing the data matrix as initial weights and random initialization.
The study is followed by an investigation into the representation capability
and the output variance of the learning scheme. An extensive experimentation on
synthetic and real-world data sets validates its numerical feasibility.
