Computer Algebra methods for matrices over rings



George Labahn, University of Waterloo, Canada. Email:

Qing-Wen Wang, Shanghai University, China. Email:

Yang Zhang, University of Manitoba, Canada. Email:


As a research area of algebra, matrices over rings, both commutative and non-commutative, have been studied for many decades. Matrices over non-commutative rings such as  quaternion and Ore algebras can be used widely in other areas like computer graphics, control theory, signal processing, physics, mechanics, and generally in solving systems of differential equations. Matrices over commutative rings, such as multivariate polynomials and power series, Dedekind domains, as well as their various projections and localizations, are also of great interest.  Associative algebras are a key tool in representation theory and factorization algorithm.  Some computer algebra based tools and algorithms for working with these matrices have been developed, for example, for efficient algorithms for computing Jacobson forms, Hermite forms and Popov forms for Ore matrices, and for computing Moore-Penrose inverses of quaternion matrices.  Many other important problems remain open and applications unaddressed.  The goal of this special session is to bring together a mixture of  researchers in algebra and computer algebra to encourage exchange of ideas and stimulate new research collaborations.

This session will therefore be devoted to work in all possible directions of symbolic and/or algebraic methods in matrices over rings and its applications, including but not limit to:

   • Algorithms for computing matrix normal forms.

   • Matrices of differential and difference and Ore polynomials

   • Equivalence and similarity problems over Ore domains

   • Eigenvalue problems in quaternion matrices.

   • Computing various generalized inverses of matrices.

   • Symbolic matrix decomposition algorithms.

   • Decomposition of associative algebras.

   • Linear algebra over skew fields.

   • Solving matrix equations.

   • Algorithms for symbolic linear and multi-linear algebra.

Call for Participation:

If you are interested in giving a presentation at this session, please send an abstract to one of the organizers by June 5, 2015.

More information can be found at ACA homepage ACA2015.