In this paper we study some aspects of new concepts introduced by D. Carfì; the new concepts are: 1) the coordinates' operator with respect to an ultralinearly indepen- dent family; 2) the product of two SL-families; 3) the invertible family; 4) the superposition of a family with respect to a family; 5) the family of change from an ultrabasis to another ultrabasis. These new concepts permit the development of a generalization of linear algebra in the space of tempered distributions and a more deeply study of some problems faced by linear algebra, as the theory of system, theory of decision, the optimal control, the quantum mechanics and so on.
On the coordinates in an ultralinearly independent family
GERMANA', CLARA;CARFI', David
2000-01-01
Abstract
In this paper we study some aspects of new concepts introduced by D. Carfì; the new concepts are: 1) the coordinates' operator with respect to an ultralinearly indepen- dent family; 2) the product of two SL-families; 3) the invertible family; 4) the superposition of a family with respect to a family; 5) the family of change from an ultrabasis to another ultrabasis. These new concepts permit the development of a generalization of linear algebra in the space of tempered distributions and a more deeply study of some problems faced by linear algebra, as the theory of system, theory of decision, the optimal control, the quantum mechanics and so on.Pubblicazioni consigliate
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