The theory and applications of the inners

The notion of the inners of a matrix is fully discussed. The inners applications to control theory, stability theory, communication theory, circuit theory, network theory, digital filters, bioengineering, sparse matrix theory, quantum physics, and some topics in mathematics are enumerated and analyzed. It is shown that the inners concept offers a theoretical as well as computational unification for these applications. In addition, the historical background and motivation is presented for the inners approach. The importance of the inners notion to education, computation, and research in system theory is surveyed and evaluated. Future research problems using this concept are enumerated. Finally, this survey is documented by many past and recent references.