Seminar

The supertropical domain is a cover of the max-plus algebra that enriches the algebraic structure and enables one to study tropical varieties directly in purely algebraic terms. It also permits one to develop matrix theory and linear algebra using methods paralleling classical algebraic techniques. In this talk we give the definition of supertropical domains and their algebraic varieities, and then turn to matrix algebra giving versions of the Hamilton-Cayley Theorem, the adjoint, Cramer's rule, eigenvectors and eigenvalues, the rank of matrices, linear dependence, and bases of tropical vector spaces.