Linear Algebra and Differential Calculus in Pseudo-Intervals Vector Space

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. 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 eigen...

Vector and Linear Algebra )

We are all familiar with the fact that if B is two miles from A, and if C is two miles from B, then C is not necessarily four miles from A. Only in very special circumstances are distances compounded according to the ordinary artimetical law of addition. Actually, there are many other entities which behave in this way as distances rather than as ordinary numbers; this motiviates the study of th...

Linear algebra and differential geometry on abstract Hilbert space

Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space Rn, Hilbert spaces admit various useful realizations as spaces of functions. In the paper this simple observation is used to construct a fruitful formalism of local coordinates on Hilbert manifolds. ...

Basics of Algebra, Topology, and Differential Calculus

Differential Equations and Linear Algebra

where D = d/dt is the basic differentiation operator on functions. (The j-th derivative operator, for j ≥ 1, is Dj , and we consider the identity operator I as D0, since it is standard to regard the zero-th derivative of a function as the function itself: D0(y) = y for all functions y.) We call (1.2) an n-th order linear differential operator since the highest derivative appearing in it is the ...