Abstract
Any system with \(n\geqslant d\) vectors from \(\mathbb{R}^{d},\) which spans \(\mathbb{R}^{d},\) is called a frame. The tight frame gives a representation of a vector from \(\mathbb{R}^{d},\) that looks like the representation in a orthonormal basis. The unitary equivalence up to a permutation on the set of tight frames preserves the inner products and is independent on the indexing of frame vectors. We present invariants of equivalence classes on the set of tight frames in \(\mathbb{R}^{d}\) , that separate classes of equivalence in general position. We describe a reconstruction of an equal norm tight frame up to permutational unitary equivalence from values of the invariants. The results are received by using the action of the symmetric group on the space of symmetric matrices. More precisely, we show algebraically independent generators of the field of invariants for this action.
