Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896414 | Journal of Algebra | 2018 | 41 Pages |
Abstract
Of special interest are the minimal realizations, which compensate the absence of a canonical form for noncommutative rational functions. The non-minimality of a realization is assessed by obstruction modules associated with it; they enable us to devise an efficient method for obtaining minimal realizations. With them we describe the stable extended domain of a noncommutative rational function and define a numerical invariant that measures its complexity. Using these results we determine concrete size bounds for rational identity testing, construct minimal symmetric realizations and prove an effective local-global principle for linear dependence of noncommutative rational functions.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jurij VolÄiÄ,