## 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.

Original language | English |
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Pages (from-to) | 73-88 |

Number of pages | 16 |

Journal | Operators and Matrices |

Volume | 8 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2014 |

## Keywords

- Diagram vectors
- Frames
- Gramian operator
- Tight frame scaling
- Tight frames