Invertible Linear Transforms Implemented by Integer Mapping

Abstract The general integer mapping theory of invertible linear transforms is considered in this paper. Two terms of integer factor and elementary triangular matrix are introduced. We prove that there exists an integer implementation if a linear transform is invertible and in finite dimensional space. The integer implementation of an invertible linear transform has several advantages such as (i) mapping integers to integers, (ii) perfectly invertible, and (iii) in-place calculation. A constructive approach of integer implementation and a simplified approach are also presented, which can be converted to some automatic steps. The error of integer implementation is estimated, and an example is given.