Inverses and eigenvalues of diamondalternating sign matrices
An n × n diamond alternating sign matrix (ASM) is a (0, +1, −1)-matrix with ±1 entries alternatingand arranged in a diamond-shaped pattern. The explicit inverse (for n even) or generalized inverse (for nodd) of a diamond ASM is derived. The eigenvalues of diamond ASMs are considered and when n is ev...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2014-02-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/spma-2014-0008 |
| _version_ | 1818676459078680576 |
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| author | Catral Minerva Lin Minghua Olesky D. D. van den Driessche P. |
| author_facet | Catral Minerva Lin Minghua Olesky D. D. van den Driessche P. |
| author_sort | Catral Minerva |
| collection | DOAJ |
| description | An n × n diamond alternating sign matrix (ASM) is a (0, +1, −1)-matrix with ±1 entries alternatingand arranged in a diamond-shaped pattern. The explicit inverse (for n even) or generalized inverse (for nodd) of a diamond ASM is derived. The eigenvalues of diamond ASMs are considered and when n is even, thecharacteristic polynomial, which involves signed binomial coefficients, is determined. |
| first_indexed | 2024-12-17T08:43:48Z |
| format | Article |
| id | doaj.art-180e18104a7e44219932d97f73cf17ef |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-12-17T08:43:48Z |
| publishDate | 2014-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-180e18104a7e44219932d97f73cf17ef2022-12-21T21:56:15ZengDe GruyterSpecial Matrices2300-74512014-02-012110.2478/spma-2014-0008spma-2014-0008Inverses and eigenvalues of diamondalternating sign matricesCatral Minerva0Lin Minghua1Olesky D. D.2van den Driessche P.3Department of Mathematics and Computer Science, Xavier University, Cincinnati,OH 45207, USADepartment of Mathematics and Statistics, University of Victoria, PO Box 1700, STN CSC, Victoria, BC, V8W 2Y2,CanadaDepartment of Computer Science, University of Victoria, PO Box 1700, STN CSC, Victoria, BC, V8W 2Y2, CanadaDepartment of Mathematics and Statistics, University of Victoria, PO Box 1700, STN CSC, Victoria, BC, V8W 2Y2,CanadaAn n × n diamond alternating sign matrix (ASM) is a (0, +1, −1)-matrix with ±1 entries alternatingand arranged in a diamond-shaped pattern. The explicit inverse (for n even) or generalized inverse (for nodd) of a diamond ASM is derived. The eigenvalues of diamond ASMs are considered and when n is even, thecharacteristic polynomial, which involves signed binomial coefficients, is determined.https://doi.org/10.2478/spma-2014-0008diamond alternating sign matrixinversegeneralized inverseeigenvaluebinomial coefficients15a0915a1815b36 |
| spellingShingle | Catral Minerva Lin Minghua Olesky D. D. van den Driessche P. Inverses and eigenvalues of diamondalternating sign matrices Special Matrices diamond alternating sign matrix inverse generalized inverse eigenvalue binomial coefficients 15a09 15a18 15b36 |
| title | Inverses and eigenvalues of diamondalternating sign matrices |
| title_full | Inverses and eigenvalues of diamondalternating sign matrices |
| title_fullStr | Inverses and eigenvalues of diamondalternating sign matrices |
| title_full_unstemmed | Inverses and eigenvalues of diamondalternating sign matrices |
| title_short | Inverses and eigenvalues of diamondalternating sign matrices |
| title_sort | inverses and eigenvalues of diamondalternating sign matrices |
| topic | diamond alternating sign matrix inverse generalized inverse eigenvalue binomial coefficients 15a09 15a18 15b36 |
| url | https://doi.org/10.2478/spma-2014-0008 |
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