On Finite Dimensional Hilbert Space Frames, Dual And Normalized Frames And Pseudo-inverse Of The Frame Operator

Abstract

In this research paper we do an introduction to Hilbert space frames. We also discuss various frames in the Hilbert space. A frame is a generalization of a basis. It is useful, for example, in signal processing. It also allows us to expand Hilbert space vectors in terms of a set of other vectors that satisfy a certain condition. This condition guarantees that any vector in the Hilbert space can be reconstructed in a numerically stable way from its frame coefficients. Our focus will be on frames in finite dimensional spaces.