Krassimir Atanassov Bulgarian Academy of Sciences, Sofia, Bulgaria Keynote title: Remarks on index matrices

Abstract

The concept of an Index Matrix (IM) was introduced in 1987 as an extension of the ordinary algebraic concept of a matrix. All operations over standard matrices are re-defined for IMs, but a lot of other specific operations, relations and operators are defined specifically over IMs. They will be described and illustrated in the presentation. Some applications of the IMs will be discussed in areas like number theory, graph theory, neural networks, decision making, cognitive maps, Big Data and others.