Natural Product Xn On Matrices

By Smarandache, Florentin

Book Id: WPLBN0002828456
Format Type: PDF eBook:
File Size: 5.24 MB
Reproduction Date: 7/31/2013

Title:	Natural Product Xn On Matrices
Author:	Smarandache, Florentin
Volume:
Language:	English
Subject:	Non Fiction, Education, Algebra
Collections:	Authors Community, Mathematics
Historic Publication Date:	2013
Publisher:	World Public Library

Member Page:	Florentin Smarandache
Citation APA MLA Chicago Smarandache, B. F., & Vasantha Kandasamy, W. B. (2013). Natural Product Xn On Matrices. Retrieved from http://www.self.gutenberg.org/

Description
This book has eight chapters. The first chapter is introductory in nature. Polynomials with matrix coefficients are introduced in chapter two. Algebraic structures on these polynomials with matrix coefficients is defined and described in chapter three. Chapter four introduces natural product on matrices. Natural product on super matrices is introduced in chapter five. Super matrix linear algebra is introduced in chapter six. Chapter seven claims only after this notion becomes popular we can find interesting applications of them. The final chapter suggests over 100 problems some of which are at research level.

Summary
In this book the authors introduce a new product on matrices called the natural product. We see when two row matrices of 1 * n order are multiplied, the product is taken component wise.

Excerpt
In this chapter we only indicate as reference of those the concepts we are using in this book. However the interested reader should refer them for a complete understanding of this book. In this book we define the notion of natural product in matrices so that we have a nice natural product defined on column matrices, m * n (m ≠ n) matrices. This extension is the same in case of row matrices. We make use of the notion of semigroups and Smarandache semigroups. Also the notion of semirings, Smarandache semirings, semi vector spaces and semifields are used.