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Supertropical quadratic forms I

Izhakian, Zur ; Knebusch, Manfred ; Rowen, Louis



Abstract

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 ...

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