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# Exploring the Extension of Natural Operations on Intervals, Matrices and Complex Numbers

## By Smarandache, Florentin

Book Id: WPLBN0002828256
Format Type: PDF (eBook)
File Size: 1.54 mb
Reproduction Date: 7/18/2013

 Title: Exploring the Extension of Natural Operations on Intervals, Matrices and Complex Numbers Author: Smarandache, Florentin Volume: Language: English Subject: Collections: Historic Publication Date: 2013 Publisher: World Public Library Member Page: Florentin Smarandache Citation APA MLA Chicago Smarandache, F., & Vasantha Kandasamy, W. B. (2013). Exploring the Extension of Natural Operations on Intervals, Matrices and Complex Numbers. Retrieved from http://self.gutenberg.org/

Description
This book extends the natural operations defined on intervals, finite complex numbers and matrices. Secondly the authors introduce the new notion of finite complex modulo numbers just defined as for usual reals. Finally we introduced the notion of natural product Xn on matrices. This enables one to define product of two column matrices of same order. We can find also product of m*n matrices even if m not does equal n. This natural product Xn is nothing but the usual product performed on the row matrices. So we have extended this type of product to all types of matrices.

Summary
The intervals [a, b] are such that a _ b. But the natural class of intervals [a, b] introduced by the authors are such that a Ñ b or a need not be comparable with b. This way of defining natural class of intervals enables the authors to extend all the natural operations defined on reals to these natural class of intervals without any difficulty. Thus with these natural class of intervals working with interval matrices like stiffness matrices finding eigen values takes the same time as that usual matrices.

Excerpt
In this chapter we just give a analysis of why we need the natural operations on intervals and if we have to define natural operations existing on reals to the intervals what changes should be made in the definition of intervals. Here we redefine the structure of intervals to adopt or extend to the operations on reals to these new class of intervals.