Vectors, pure and applied : a general introduction to linear algebra /

Vectors, pure and applied : a general introduction to linear algebra /

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Bibliographic Details
Author / Creator:Körner, T. W. (Thomas William), 1946- author.
Imprint:Cambridge : Cambridge University Press, 2013.
Description:1 online resource (xii, 444 pages) : illustrations
Language:English
Subject:
Vector algebra.
Algebras, Linear.
Algebras, Linear.
Vector algebra.
Electronic book.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11831431
Hidden Bibliographic Details
ISBN:9781139626156
1139626159
9781139520034
1139520032
9781283871006
1283871009
9781139622431
1139622439
9781139616850
1139616854
9781107033566
110703356X
9781107675223
1107675227
1107238277
9781107238275
1107255023
9781107255029
1139611275
9781139611275
1139613138
9781139613132
Notes:Includes bibliographical references and index.
English.
Print version record.
Summary:"Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online"--
Other form:Print version: Körner, T.W. (Thomas William), 1946- Vectors, pure and applied. Cambridge : Cambridge University Press, 2013 9781107033566

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100 1 |a Körner, T. W.  |q (Thomas William),  |d 1946-  |e author.  |0 http://id.loc.gov/authorities/names/n85062597 
245 1 0 |a Vectors, pure and applied :  |b a general introduction to linear algebra /  |c T.W. Körner. 
260 |a Cambridge :  |b Cambridge University Press,  |c 2013. 
300 |a 1 online resource (xii, 444 pages) :  |b illustrations 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
504 |a Includes bibliographical references and index. 
505 0 0 |g Part I.  |t Familiar vector spaces --  |g 1.  |t Gaussian elimination --  |t Two hundred years of algebra --  |t Computational matters --  |t Detached coefficients --  |t Another fifty years --  |g 2.  |t A little geometry --  |t Geometric vectors --  |t Higher dimensions --  |t Euclidean distance --  |t Geometry, plane and solid --  |g 3.  |t The algebra of square matrices --  |t The summation convention --  |t Multiplying matrices --  |t More algebra for square matrices --  |t Decomposition into elementary matrices --  |t Calculating the inverse --  |g 4.  |t The secret life of determinants --  |t The area of a parallelogram --  |t Rescaling --  |t 3 x 3 determinants --  |t Determinants of n × n matrices --  |t Calculating determinants --  |g 5.  |t Abstract vector spaces --  |t The space Cn --  |t Abstract vector spaces --  |t Linear maps --  |t Dimension --  |t Image and kernel --  |t Secret sharing --  |g 6.  |t Linear maps from Fn to itself --  |t Linear maps, bases and matrices --  |t Eigenvectors and eigenvalues --  |t Diagonalisation and eigenvectors --  |t Linear maps from C2to itself --  |t Diagonalising square matrices --  |t Iteration's artful aid --  |t LU factorisation --  |g 7.  |t Distance preserving linear maps --  |t Orthonormal bases --  |t Orthogonal maps and matrices --  |t Rotations and reflections in R2and R3 --  |t Reflections in Rn --  |t QR factorisation --  |g 8.  |t Diagonalisation for orthonormal bases --  |t Symmetric maps --  |t Eigenvectors for symmetric linear maps --  |t Stationary points --  |t Complex inner product --  |g 9.  |t Cartesian tensors --  |t Physical vectors --  |t General Cartesian tensors --  |t More examples --  |t The vector product --  |g 10.  |t More on tensors --  |t Some tensorial theorems --  |t A (very) little mechanics --  |t Left-hand, right-hand --  |t General tensors --  |g Part II.  |t General vector spaces --  |g 11.  |t Spaces of linear maps --  |t A look at L(U, V) --  |t A look at L(U, U) --  |t Duals (almost) without using bases --  |t Duals using bases --  |g 12.  |t Polynomials in L(U, U) --  |t Direct sums --  |t The Cayley-Hamilton theorem --  |t Minimal polynomials --  |t The Jordan normal form --  |t Applications --  |g 13.  |t Vector spaces without distances --  |t A little philosophy --  |t Vector spaces over fields --  |t Error correcting codes --  |g 14.  |t Vector spaces with distances --  |t Orthogonal polynomials --  |t Inner products and dual spaces --  |t Complex inner product spaces --  |g 15.  |t More distances --  |t Distance on L(U, U) --  |t Inner products and triangularisation --  |t The spectral radius --  |t Normal maps --  |g 16.  |t Quadratic forms and their relatives --  |t Bilinear forms --  |t Rank and signature --  |t Positive definiteness --  |t Antisymmetric bilinear forms --  |t Further exercises. 
520 |a "Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online"--  |c Provided by publisher. 
588 0 |a Print version record. 
546 |a English. 
650 0 |a Vector algebra.  |0 http://id.loc.gov/authorities/subjects/sh85142448 
650 0 |a Algebras, Linear.  |0 http://id.loc.gov/authorities/subjects/sh85003441 
650 7 |a MATHEMATICS  |x Algebra  |x General.  |2 bisacsh 
650 7 |a MATHEMATICS  |x Geometry  |x General.  |2 bisacsh 
650 7 |a Algebras, Linear.  |2 fast  |0 (OCoLC)fst00804946 
650 7 |a Vector algebra.  |2 fast  |0 (OCoLC)fst01164648 
655 0 |a Electronic book. 
655 4 |a Electronic books. 
776 0 8 |i Print version:  |a Körner, T.W. (Thomas William), 1946-  |t Vectors, pure and applied.  |d Cambridge : Cambridge University Press, 2013  |z 9781107033566  |w (DLC) 2012036797  |w (OCoLC)809611894 
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928 |t Library of Congress classification  |a QA200 .K67 2013eb  |l Online  |c UC-FullText  |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=508905  |z eBooks on EBSCOhost  |g ebooks  |i 12379943 

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