Matrix representations of linear transformations on bicomplex space

An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The elements of this space are linear maps of a special form. These linear maps are examined with respect to usual notions like kernel, range, and singularity. Their matrix representation is also discussed.