  By a tensor we mean an element of a tensor product of vector spaces over a
field. Up to a choice of bases in factors of tensor products, every tensor may
be coordinatized, that is, represented as an array consisting of numbers. This
note is concerned with properties of the~tensor rank that is a natural
generalization of the matrix rank. The topological group structure of
invertible matrices is involved in this study. The multilinear matrix
multiplication is discussed from a viewpoint of transformation groups. We treat
a low-rank tensor approximation in finite-dimensional tensor products. It is
shown that the problem on determining a best rank-$n$ approximation for a
tensor of size $n\times n \times 2$ has no a solution.To this end, we make use
of an~approximation by matrices with simple spectra.
