The Linearly Independent Non Orthogonal yet Energy Preserving (LINOEP) vectors

Abstract

It is well known that, in any inner product space, a set of linearly independent (LI) vectors can be transformed to a set of orthogonal vectors, spanning the same space, by the Gram-Schmidt Orthogonalization Method (GSOM). In this paper, we propose a transformation from a set of LI vectors to a set of LI non orthogonal yet energy (square of the norm) preserving (LINOEP) vectors in an inner product space and we refer it as LINOEP method. We also show that there are various solutions to preserve the square of the norm.