# Interval Linear Algebra by W. B. Vasantha Kandasamy, Florentin Smarandache

By W. B. Vasantha Kandasamy, Florentin Smarandache

Period mathematics, or period arithmetic, was once built within the Nineteen Fifties and Sixties as an method of rounding error in mathematical computations. even if, there has been no methodical improvement of period algebraic buildings to this date. This publication presents a scientific research of period algebraic constructions, viz. period linear algebra, utilizing durations of the shape [0, a].

Read Online or Download Interval Linear Algebra PDF

Best linear books

A first course in linear algebra

A primary path in Linear Algebra is an creation to the elemental thoughts of linear algebra, besides an advent to the thoughts of formal arithmetic. It starts with platforms of equations and matrix algebra ahead of getting into the speculation of summary vector areas, eigenvalues, linear alterations and matrix representations.

Measure theory/ 3, Measure algebras

Fremlin D. H. degree thought, vol. three (2002)(ISBN 0953812936)(672s)-o

Elliptic Partial Differential Equations

Elliptic partial differential equations is without doubt one of the major and so much energetic components in arithmetic. In our ebook we research linear and nonlinear elliptic difficulties in divergence shape, with the purpose of offering classical effects, in addition to more moderen advancements approximately distributional options. hence the e-book is addressed to master's scholars, PhD scholars and a person who desires to start learn during this mathematical box.

Additional resources for Interval Linear Algebra

Sample text

The map T: R o S is defined by T([0, n]) = [0, n], n  Z+  {0} is a semigroup interval linear transformation. 26: Let R = {[n, 5n] | n  Z+  {0}} and S = {[n, 5n] | n  R+  {0}} be two semigroup interval linear algebras defined over the semigroup F = Z+  {0}. Define T: Ro S by T {[n, 5n]} = [n, 5n], for all [n, 5n]  R. It is easily verified T is a semigroup interval linear transformation of R to S and infact T is an embedding. We will give an example of a semigroup interval linear operator.

Let S = {[0, n] | n  Z36} be a semigroup interval vector space of S over the semigroup Z36 = F. Choose P1 = {[0, 2n] |n  Z36} = {[0, 0], [0, 2], [0, 4], [0, 6], I ; P1 is a semigroup interval vector subspace …, [0, 34]}  Z36 of S over the semigroup F = Z36. P2 = {[0, 4n] | n  Z36} = {[0, 0], [0, 4], [0, 8], [0, 12], [0, 16], [0, 20], [0, 24], [0, 28]}  S is a semigroup interval vector subspace of S over the semigroup F 32 = Z36. P3 = {[0, 3n] / n  Z36}  S is a semigroup interval vector subspace of S over F = Z36.

Now we will proceed onto define the notion of semigroup linearly independent linearly dependent interval subset of a semigroup interval vector space. 3: Let S be a semigroup interval vector space over the semigroup F. A set of interval elements B = {s1, s2, …, sn} of S is a said to be a semigroup linearly independent interval subset if si z csj; for all c  F and si, sj  B; i z j; 1 d i, j d n. If for some si = csj, c  F; izj; si, sj  B then we say the semigroup interval subset is linearly dependent or not linearly independent.

Download PDF sample

Rated 4.66 of 5 – based on 9 votes