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 de...
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| creator | Copenhaver, Martin S Yeon Hyang Kim Logan, Cortney Mayfield, Kyanne Narayan, Sivaram K Petro, Matthew J Sheperd, Jonathan |
| description | 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. |
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| subjects | Frames Hilbert space Polar coordinates Scaling Vector spaces |
| title | Diagram vectors and Tight Frame Scaling in Finite Dimensions |
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