  We consider frames in a finite-dimensional Hilbert space Hn where frames are
exactly the spanning sets of the vector space. The diagram vector of a vector
in R2 was previously defined using polar coordinates and was used to
characterize tight frames in R2 in a geometric fashion. Reformulating the
definition of a diagram vector in R2 we provide a natural extension of this
notion to Rn and Cn. Using the diagram vectors we give a characterization of
tight frames in Rn or Cn. Further we provide a characterization of when a
unit-norm frame in Rn or Cn can be scaled to a tight frame. This classification
allows us to determine all scaling coefficients that make a unit-norm frame
into a tight frame.
