Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diagram vectors and Tight Frame Scaling in Finite Dimensions   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.

7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics