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doi:10.22028/D291-47572 | Title: | Computing the Noncommutative Inner Rank by Means of Operator-Valued Free Probability Theory |
| Author(s): | Hoffmann, Johannes Mai, Tobias Speicher, Roland |
| Language: | English |
| Title: | Foundations of Computational Mathematics |
| Volume: | 26 (2026) |
| Issue: | 1 |
| Pages: | 313-348 |
| Publisher/Platform: | Springer Nature |
| Year of Publication: | 2024 |
| Free key words: | Noncommutative inner rank Noncommutative Edmonds’ problem Free probability theory Operator-valued semicircular elements |
| DDC notations: | 510 Mathematics |
| Publikation type: | Journal Article |
| Abstract: | We address the noncommutative version of the Edmonds’ problem, which asks to determine the inner rank of a matrix in noncommuting variables. We provide an algo rithm for the calculation of this inner rank by relating the problem with the distribution of a basic object in free probability theory, namely operator-valued semicircular ele ments. We have to solve a matrix-valued quadratic equation, for which we provide precise analytical and numerical control on the fixed point algorithm for solving the equation. Numerical examples show the efficiency of the algorithm. |
| DOI of the first publication: | 10.1007/s10208-024-09684-5 |
| URL of the first publication: | https://doi.org/10.1007/s10208-024-09684-5 |
| Link to this record: | urn:nbn:de:bsz:291--ds-475724 hdl:20.500.11880/41600 http://dx.doi.org/10.22028/D291-47572 |
| ISSN: | 1615-3383 1615-3375 |
| Date of registration: | 27-Apr-2026 |
| Faculty: | MI - Fakultät für Mathematik und Informatik |
| Department: | MI - Mathematik |
| Professorship: | MI - Prof. Dr. Roland Speicher |
| Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| s10208-024-09684-5.pdf | 1,03 MB | Adobe PDF | View/Open |
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