MITACS Seminar Series on Mathematics of Computer Algebra and Analysis
Normal Forms of Polynomial Matrices
Howard Cheng, Department of Mathematics and Computer Science, University of Lethbridge
Abstract: Normal forms for polynomial matrices are used in applications such as control theory. The Hermite form, row-reduced form, weak Popov form and Popov form are introduced. It is shown how these normal forms can be computed by straightforward elimination-based algorithms. In many cases, elimination-based approaches are insufficient because of intermediate expression swell on the coefficients. Fraction-free and modular algorithms for these problems are briefly outlined.