Some 'What', 'Why' and 'How' on Row Reducing Matrices over Ore Polynomial Rings

Ore polynomials, also known as skew polynomials, are non-commutative polynomial which can algebraically model differential equations, time-dependent systems, linear maps over finite fields, and more. Matrices over Ore polynomial rings can model systems of these objects and have found applications in diverse areas. Computing normal forms of such matrices can be useful for checking system equivalence or finding special elements in the space, e.g. shortest vectors.

In this talk I will introduce Ore polynomial rings, some important examples hereof, and describe some recent work on computing certain reduced normal forms of matrices of Ore polynomials.