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This paper considers an idempotent and symmetrical algebraic structure aswell as some closely related concept. A special notion of determinant isintroduced and a Cramer formula is derived for a class of limit systems derivedfrom the Hadamard matrix product and we give the algebraic form of a sequenceof hyperplanes passing through a finite number of points. Thereby, somestandard results arising for Max-Times systems with nonnegative entries appearas a special case. The case of two sided systems is also analyzed. In addition,a notion of eigenvalue in limit is considered. It is shown that one canconstruct a special semi-continuous regularized polynomial to find theeigenvalues of a matrix with nonnegative entries.

Determinants and Limit Systems in some Idempotent and Non-Associative Algebraic Structure