Fast linearly independent arithmetic expansions

The concept of Linearly Independent arithmetic (LIA) transforms and expansi ons is introduced in this paper. The recursive ways of generating forward a nd inverse fast transforms for LIA are presented. The paper describes basic properties and lists those LIA transforms which have convenient fast forwa rd algorithms and easily defined inverse transforms. In addition, those tra nsforms which require horizontal or vertical permutations to have fast tran sform are also discussed. The computational advantages and usefulness of ne w expansions based on LIA logic in comparison to known arithmetic expansion s are discussed.