The paper is extremely interesting and important. It is well known that certain problems of linear algebra (such as classification of pairs of linear maps) are hopeless. Therefore the study has been restricted to manageable problems. One of the results of the corresponding theory is that dimension vectors of indecomposable representations of tame graphs are positive roots of affine Kac-Moody Lie algebras. The author shows that a similar result holds for a much larger class of graphs. Thus, although we cannot describe all the representations of such graphs we still can describe all possible dimension vectors (as positive roots of arbitrary Kac-Moody Lie algebra). Moreover, all indecomposable representations whose dimension vector is a given real root are equivalent. Thus, the problem is unmanageable only if its dimension vector is an imaginary root. The proof of this result involves several ingredients. Most important of them is the study of the action of some linear group on the set of representations. This leads the author to a conjecture about connections between the actions of a linear group on a vector space and its dual. He proves the conjecture for finite fields and it suffices, it turns out, for his purposes. The general case is still open. The paper contains other important and interesting results and observations.