The Libraries will be performing routine maintenance on UWSpace on October 20th, 2025, from 10:00-10:30 pm ET. UWSpace will be unavailable during this time. Service should resume by 10:30 pm ET.
 

Computing Popov Forms of Polynomial Matrices

Loading...
Thumbnail Image

Date

2012-01-19T18:13:17Z

Authors

Sarkar, Soumojit

Advisor

Journal Title

Journal ISSN

Volume Title

Publisher

University of Waterloo

Abstract

This thesis gives a deterministic algorithm to transform a row reduced matrix to canon- ical Popov form. Given as input a row reduced matrix R over K[x], K a field, our algorithm computes the Popov form in about the same time as required to multiply together over K[x] two matrices of the same dimension and degree as R. Randomization can be used to extend the algorithm for rectangular input matrices of full row rank. Thus we give a Las Vegas algorithm that computes the Popov decomposition of matrices of full row rank. We also show that the problem of transforming a row reduced matrix to Popov form is at least as hard as polynomial matrix multiplication.

Description

Keywords

LC Subject Headings

Citation