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Bakhadly, B. and Guterman, A. and Puente Muñoz, María Jesús de la (2023) Normal Tropical (0,−1)-Matrices and Their Orthogonal Sets. Journal of Mathematical Sciences, 269 (5). pp. 614-631. ISSN 1072-3374
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Official URL: https://doi.org/10.1007/s10958-023-06305-4
Abstract
Square matrices A and B are orthogonal if AʘB = Z = BʘA, where Z is the matrix entries equal to 0, and ʘ is the tropical matrix multiplication. We study orthogonality for normal matrices over the set {0, −1}, endowed with tropical addition and multiplication. To do this, we investigate the orthogonal set of a matrix A, i.e., the set of all matrices orthogonal to A. In particular, we study the family of minimal elements inside the orthogonal set, called a basis. Orthogonal sets and bases are computed for various matrices and matrix sets. Matrices whose bases are singletons are characterized. Orthogonality and minimal orthogonality are described in the language of graphs. The geometric interpretation of the results obtained is discussed.
| Item Type: | Article |
|---|---|
| Additional Information: | Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 24, No. 1, pp. 5–30, 2022. |
| Uncontrolled Keywords: | Orthogonal; Orthogonality; Tropical semiring; Tropical normal matrix |
| Subjects: | Sciences > Mathematics > Algebra |
| ID Code: | 76951 |
| Deposited On: | 08 Mar 2023 15:27 |
| Last Modified: | 08 Mar 2023 15:27 |
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