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Linear Algebra in the vector space of intervals
TLDR
A notion of central eigenvalues permits to describe criterium of diagonalization of square matrices whose coefficients are intervals and a notion of Exponential mapping is defined.Abstract:
In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. 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). We consider a notion of central eigenvalues permits to describe criterium of diagonalization. As application, we define a notion of Exponential mapping.read more
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Dissertation
N-ary algebras. Arithmetic of intervals
TL;DR: In this article, the authors define a partielle associative 3-aire partiellement associative, i.e., a productit interne sur des matrices non carrees.
n-ary algebras. Intervals arithmetic
TL;DR: In this paper, a mémoire comporte de two parties distinctes: the partie partie concerne uné etude d'algèbres n-aires.
Journal ArticleDOI
Interval Linear Algebra - A New Perspective
TL;DR: In this article , the authors put the concept of interval linear algebra on a sound algebraic setting, by judiciously defining a Field and a Vector Space over a field involving equivalence classes.
Generalized difference sequence spaces of modal interval numbers defined by a sequence of modulus functions
S. Zion Chella Ruth,K. Vembarasi +1 more
TL;DR: In this paper, the generalized difference sequence spaces of modal interval numbers were introduced and investigated, defined by a sequence of modulus functions and p=(p k ) being any bounded sequence of positive real numbers.
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Diagonal canonical form of interval matrices and applications on dynamical systems
T. Nirmala,K. Ganesan +1 more
TL;DR: In this article , the pairing technique is used for diagonalizing interval matrices, which will make it simpler and more effective to classify and investigate interval matrix matrices and is applied to planar systems and linear discrete dynamical systems.
References
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Posted Content
An algebraic approach to the set of intervals
Nicolas Goze,Elisabeth Remm +1 more
TL;DR: A four-dimensional associative algebra whose product gives the product of intervals in any cases is defined, which allows to give a notion of divisibility and in some cases an euclidian division.
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