  In this paper the main results in arXiv:0901.3179v3, related to the matrix
representation of polynomial maps, are restated in traditional way of linear
algebra assuming that variable vectors are presented as column vectors. Some
new results related to that subject are also included. Here one can find the
behavior of the matrices of polynomial maps with respect to the change of
variables (coordinate system), matrix representations for symmetric and
antisymmetric multi-linear maps. It is shown also that the offered
representations are in good concordance with known operations over such
multi-linear maps.
