Unimodular Completions and Orthogonal Complements of Matrices over Univariate Ore Extensions
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
We generalize an efficient hyper-regularity and unimodularity test from differential Ore polynomial matrices to arbitrary Ore polynomial matrices. The core of the contribution consists of algorithms for unimodular row and column completions of arbitrary univariate Ore polynomial matrices, respectively. After a possible degree reduction using noncommutative companion matrices, this is done by a systematic projection of suitable coordinates with a subsequent elimination. Based on previous work for differential Ore polynomial matrices, we remove rather restrictive conditions, which now allows for the application of this algorithm to a larger class of systems that may contain pure algebraic equations.
Details
Original language | English |
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Pages (from-to) | 128-155 |
Number of pages | 28 |
Journal | SIAM Journal on Matrix Analysis and Applications |
Volume | 44 |
Issue number | 1 |
Publication status | Published - 2023 |
Peer-reviewed | Yes |
External IDs
Scopus | 85151058718 |
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WOS | 000974412700004 |
Mendeley | 8163a649-a1d4-3703-88b8-ada7e3b6ecc3 |
Keywords
Research priority areas of TU Dresden
ASJC Scopus subject areas
Keywords
- Algorithms, Hyper-regularity, Ore extensions, Ore polynomial matrices, Pseudolinear algebra, Unimodularity, algorithms, pseudolinear algebra, hyper-regularity, unimodularity