Izhakian, Zur and Knebusch, Manfred and Rowen, Louis (2016) Supertropical quadratic forms I. JOURNAL OF PURE AND APPLIED ALGEBRA, 220 (1). pp. 61-93. ISSN 0022-4049, 1873-1376
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We initiate the theory of a quadratic form q over a semiring R, with a view to study tropical linear algebra. As customary, one can write q(x + y) = q(x) + q(y) + b(x,y), where b is a companion bilinear form. In contrast to the classical theory of quadratic forms over a field, the companion bilinear form need not be uniquely defined. Nevertheless, q can always be written as a sum of quadratic forms q = q(QL) + rho, where q(QL) is quasilinear in the sense that q(QL)(x y) = q(QL)(x) + q(QL)(y), and rho is rigid in the sense that it has a unique companion. In case that R is supertropical, we obtain an explicit classification of these decompositions q = q(QL) + rho and of all companions b of q, and see how this relates to the tropicalization procedure. (C) 2015 Elsevier B.V. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MATRIX ALGEBRA; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Manfred Knebusch |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 01 Mar 2019 12:36 |
| Last Modified: | 11 Mar 2019 12:31 |
| URI: | https://pred.uni-regensburg.de/id/eprint/2265 |
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