Add to Book Shelf
Flag as Inappropriate
Email this Book

DSm Super Vector Space of Refined Labels : Volume 2

By Kandasamy, W. B. Vasantha

Click here to view

Book Id: WPLBN0002828222
Format Type: PDF eBook:
File Size: 7.75 MB
Reproduction Date: 7/17/2013

Title: DSm Super Vector Space of Refined Labels : Volume 2  
Author: Kandasamy, W. B. Vasantha
Volume: 2
Language: English
Subject: Non Fiction, Education, Super Vector
Collections: Mathematics, Algebra, Authors Community, Math, Literature, Most Popular Books in China, Favorites in India, Education
Publication Date:
Publisher: World Public Library
Member Page: Florentin Smarandache


APA MLA Chicago

B. Vasantha Kandasam, B. W., & Smarandache, F. (2013). DSm Super Vector Space of Refined Labels : Volume 2. Retrieved from

In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m Å~ n matrix of refined labels are introduced and studied. We mainly study this to introduce to super vector space of refined labels using matrices.

We in this book introduce the notion of semifield of refined labels using which we define for the first time the notion of supersemivector spaces of refined labels. Several interesting properties in this direction are defined and derived.

THEOREM 1.1.1: Let S = {(a1 a2 a3 | a4 a5 | a6 a7 a8 a9 | … | an-1, an) | ai ∈ R; 1 ≤ i ≤ n} be the collection of all super row vectors with same type of partition, S is a group under addition. Infact S is an abelian group of infinite order under addition. The proof is direct and hence left as an exercise to the reader. If the field of reals R in Theorem 1.1.1 is replaced by Q the field of rationals or Z the integers or by the modulo integers Zn, n < ∞ still the conclusion of the theorem 1.1.1 is true. Further the same conclusion holds good if the partitions are changed. S contains only same type of partition. However in case of Zn, S becomes a finite commutative group.


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.