Linear Algebra in the vector space of intervals

In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. For example, we define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with respect to the real case, a matrix of order n could have more than n eigenvalues (the set of intervals is not factorial). But we define a notion of central eigenvalues this permits to describe criterium of diagonalization. We end this paper with the notion of Exponential mapping. 1 The associative algebra IR In [1], we have given a representation of the set of intervals in terms of associative algebra. More precisely, we define on the set IR of intervals of R a R-vector space structure. Next we embed IR in a 4dimensional associative algebra. This embedding permits to describe a unique distributive multiplication which contains all the possible results of the usual product of intervals. Recall that this usual product is not distributive wi...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Nicolas Goze
• Keywords: Associative Algebra, Associative Algebra Ir, CORR 2010, Education, Usual Product