Abstract. We consider frames in a finite-dimensional Hilbert space H n where frames are exactly the spanning sets of the vector space. The diagram vector of a vector in R 2 was previously defined using polar coordinates and was used to characterize tight frames in R 2 in a geometric fashion. Reformulating the definition of a diagram vector in R 2 we provide a natural extension of this notion to R n and C n . Using the diagram vectors we give a characterization of tight frames in R n or C n . Further we provide a characterization of when a unit-norm frame in R n or C n 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. Mathematics subject classification (2010): 42C15, 05B20, 15A03.

Abstract. We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. We present a method to determine the maximum robustness of a frame. We present results on tight subframes and surgery of frames. We also answer the question of when length surgery resulting in a tight frame set for Hn is possible.

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