  A unitary (Euclidean) representation of a quiver is given by assigning to
each vertex a unitary (Euclidean) vector space and to each arrow a linear
mapping of the corresponding vector spaces. We recall an algorithm for reducing
the matrices of a unitary representation to canonical form, give a certain
description of the representations in canonical form, and reduce the problem of
classifying Euclidean representations to the problem of classifying unitary
representations. We also describe the set of dimensions of all indecomposable
unitary (Euclidean) representations of a quiver and establish the number of
parameters in an indecomposable unitary representation of a given dimension.
