An edition of Tensor analysis for physicists (1951)

Tensor analysis for physicists

2nd ed.
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Last edited by MARC Bot
November 6, 2020 | History
An edition of Tensor analysis for physicists (1951)

Tensor analysis for physicists

2nd ed.
  • 7 Want to read

When we represent data for machine learning, this generally needs to be done numerically. Especially when referring specifically of neural network data representation, this is accomplished via a data repository known as the tensor. A tensor is a container which can house data in N dimensions. Often and erroneously used interchangeably with the matrix (which is specifically a 2-dimensional tensor), tensors are generalizations of matrices to N-dimensional space.
Mathematically speaking, tensors are more than simply a data container, however. Aside from holding numeric data, tensors also include descriptions of the valid linear transformations between tensors. Examples of such transformations, or relations, include the cross product and the dot product. From a computer science perspective, it can be helpful to think of tensors as being objects in an object-oriented sense, as opposed to simply being a data structure.
The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapter VII, modern tensor calculus is applied to some old and some modern problems of elasticity and piezo-electricity. Chapter VIII presents examples concerning anholonomic systems and the homogeneous treatment of the equations of Lagrange and Hamilton. Chapter IX deals first with relativistic kinematics and dynamics, then offers an exposition of modern treatment of relativistic hydrodynamics. Chapter X introduces Dirac’s matrix calculus. Two especially valuable features of the book are the exercises at the end of each chapter, and a summary of the mathematical theory contained in the first five chapters — ideal for readers whose primary interest is in physics rather than mathematics.

Publish Date
Publisher
Dover Publications
Language
English
Pages
277

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Previews available in: English

Edition Availability
Cover of: Tensor analysis for physicists
Tensor analysis for physicists
1989, Dover Publications
in English - 2nd ed.
Cover of: Tensor analysis for physicists
Tensor analysis for physicists
1954, Clarendon Press
in English - 2d ed.
Cover of: Tensor analysis for physicists.
Tensor analysis for physicists.
1951, Clarendon Press
in English

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Book Details


Edition Notes

Bibliography: p. [268]-271.
Reprint. Originally published: 2nd ed. Oxford : Clarendon Press, 1954.
Includes index.

Published in
New York

Classifications

Dewey Decimal Class
515/.63
Library of Congress
QC20.7.C28 S36 1989, QC20.7.C28S36 1989

The Physical Object

Pagination
xii, 277 p. :
Number of pages
277

ID Numbers

Open Library
OL2405491M
Internet Archive
isbn_9780486655826
ISBN 10
0486655822
LCCN
87036451
Library Thing
2273081
Goodreads
2302576

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November 6, 2020 Edited by MARC Bot import existing book
October 7, 2020 Edited by ImportBot import existing book
July 31, 2020 Edited by ImportBot import existing book
January 19, 2016 Edited by ImportBot import new book
April 1, 2008 Created by an anonymous user Imported from Scriblio MARC record