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PDF free download --subject to stated copyright permissions, over 1Mb text in 13 Chapters w. Appendices, Software, 2007-2k8

Abstract:

Contains also Clifford Algebra and matrix representations in addition to powerful Mathematica(TM)-based software for concrete/specific applications listed next. Bibliography and Grassmann's Biography also included Author's Abstract and presentation of the book--as quotes, including software: ...''The focus of this book: The primary focus of this book is to provide a readable account in modern notation of Grassmann' s major algebraic contributions to mathematics and science.'' ...``accessible to scientists and engineers, students and professionals alike''. ... ``tried to avoid all mathematical terminology which does not make an essential contribution to understanding the basic concepts. The only assumptions... made as to the reader' s background is that they have some familiarity with basic linear algebra. The secondary concern of this book is to provide an environment for exploring applications of the Grassmann algebra. For general applications in higher dimensional spaces, computations by hand in any algebra become tedious, indeed limiting, thus restricting the hypotheses that can be explored. For this reason the book includes a package for exploring Grassmann algebra, called GrassmannAlgebra, which may be found on the CD at the back of the book. GrassmannAlgebra has been developed in Mathematica. You can read the book without using the package, or you can use the package to extend the examples in the text, experiment with hypotheses, or explore your own interests.'' `` What is Grassmann algebra? The intrinsic power of Grassmann algebra arises from its fundamental product operation, the exterior product. The exterior product codifies the property of linear dependence, so essential for modern applied mathematics, directly into the algebra. Simple non-zero elements of the algebra may be viewed as representing constructs of linearly independent elements. For example, a simple bivector is the exterior product of two vectors; a line is the exterior product of two points and a plane is the exterior product of three points. The power of Mathematica : Mathematica ...TM (Wolfram Research Co, Champaign, USA)...`` is a powerful system for doing mathematics on a computer. It has an inbuilt programming language ideal for extending its capabilities to other mathematical systems like Grassmann algebra. It also has a sophisticated mathematical typesetting capability. This book uses both. The chapters are typeset by Mathematica in its standard notebook format, making the book interactive in its electronic version with the GrassmannAlgebra package. GrassmannAlgebra can turn an exploration requiring days by hand into one requiring just minutes of computing time. How you can use this book Chapter 1: Introduction provides a brief preparatory overview of the book;... Finally, the term `GrassmannAlgebra will be used to refer to the Mathematica based software package which accompanies it.\\\ Some of the things you can do with the GrassmannAlgebra software. You can: Set up your own space of any dimension and metric. The default is a three-dimensional Euclidean space. Work basis-free or with a basis as appropriate. Declare your own scalar symbols: symbols or symbol patterns you want specially interpreted as scalars. Declare your own vector symbols: symbols or symbol patterns you want specially interpreted as vectors. Apply Grassmann operations. A Grassmann operation is any of: the complement operation and the six product operations: the exterior, regressive, interior, generalized Grassmann, hypercomplex and Clifford products. Manipulate Grassmann expressions and numbers. A Grassmann expression is either a scalar, a Grassmann variable, or the result of a sequence of Grassmann operations or sums on Grassmann expressions. A Grassmann number is a Grassmann expression expressed as a linear combination of basis elements. Compute the grade of any Grassmann expression. For example the grade of an expression which reduces to the sum of a scalar, vector and bivector would be computed as {0, 1, 2}. Query the attributes of any expression. For example, is it: a Grassmann expression? a scalar? a Grassmann variable? a basis element? a metric element? of grade m? of even grade? of odd grade? the soul of a Grassmann expression? an interior product? an inner product? a scalar product? Extract components of different types from Grassmann expressions. For example extract: scalars, basis elements, metric elements, Grassmann variables, elements of even grade, elements of odd grade, elements of grade m, the body, the soul. Convert Grassmann expressions from one form to another. For example you can: Expand products of sums'',... http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/TitlePage.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/TableOfContents.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/Introduction.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/TheExteriorProduct.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/TheRegressiveProduct.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/GeometricInterpretations.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/TheComplement.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/TheInteriorProduct.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/ExploringScrewAlgebra.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/ExploringMechanics.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/ExploringGrassmannAlgebra.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/ExpTheGeneralizedProduct.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/ExpHypercomplexAlgebra.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/ExploringCliffordAlgebra.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/ExpGrassmannMatrixAlgebra.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/ABriefBiographyOfGrassmann.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/Notation.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/Glossary.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/bookpdf/Bibliography.pdf http://www.grassmannalgebra.info/grassmannalgebra/book/index.htm http://www.grassmannalgebra.info/grassmannalgebra/book/index.htm#Software http://www.grassmannalgebra.info/index.htm

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Open access only for individual study: Copyright @ John M Browne 2007 http://www.grassmannalgebra.info/grassmannalgebra/book/index.htm http://www.grassmannalgebra.info/index.htm ''Copyright agreement: All the chapters you see available here are of course protected by copyright. It is a condition of your accessing the files that you agree to use them for your own individual private study only. They may not otherwise be copied or distributed in any way in whole or in part without the permission of the author. You may reference or quote small sections of the work as long as due acknowledgment is made.'' John M Browne

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