Interval linear algebra – A new perspective

Abstract

The purpose of this article is to put the concept of interval linear algebra on a sound algebraic setting, by judiciously defining a Field and a Vector Space over a field involving equivalence classes. Classifying mathematical objects by bringing them into canonical forms, is an important subject of study in every branch of Mathematics. The concepts of eigenvalues and eigenvectors are used in several fields including machine learning, quantum computing, communication system design, construction design, electrical and mechanical engineering etc. The study of interval matrices leads to canonical forms of interval matrices, which will help us classify and study interval matrices more effectively and more easily.

Keywords

• Interval
• Interval matrix
• Equivalance relation
• Eigenvalues
• Eigenvectors
• Canonical forms