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

Table of Contents:

Part I. Familiar vector spaces
1. Gaussian elimination
Two hundred years of algebra
Computational matters
Detached coefficients
Another fifty years
2. A little geometry
Geometric vectors
Higher dimensions
Euclidean distance
Geometry, plane and solid
3. The algebra of square matrices
The summation convention
Multiplying matrices
More algebra for square matrices
Decomposition into elementary matrices
Calculating the inverse
4. The secret life of determinants
The area of a parallelogram
Rescaling
3 x 3 determinants
Determinants of n × n matrices
Calculating determinants
5. Abstract vector spaces
The space Cn
Abstract vector spaces
Linear maps
Dimension
Image and kernel
Secret sharing
6. Linear maps from Fn to itself
Linear maps, bases and matrices
Eigenvectors and eigenvalues
Diagonalisation and eigenvectors
Linear maps from C2to itself
Diagonalising square matrices
Iteration's artful aid
LU factorisation
7. Distance preserving linear maps
Orthonormal bases
Orthogonal maps and matrices
Rotations and reflections in R2and R3
Reflections in Rn
QR factorisation
8. Diagonalisation for orthonormal bases
Symmetric maps
Eigenvectors for symmetric linear maps
Stationary points
Complex inner product
9. Cartesian tensors
Physical vectors
General Cartesian tensors
More examples
The vector product
10. More on tensors
Some tensorial theorems
A (very) little mechanics
Left-hand, right-hand
General tensors
Part II. General vector spaces
11. Spaces of linear maps
A look at L(U, V)
A look at L(U, U)
Duals (almost) without using bases
Duals using bases
12. Polynomials in L(U, U)
Direct sums
The Cayley-Hamilton theorem
Minimal polynomials
The Jordan normal form
Applications
13. Vector spaces without distances
A little philosophy
Vector spaces over fields
Error correcting codes
14. Vector spaces with distances
Orthogonal polynomials
Inner products and dual spaces
Complex inner product spaces
15. More distances
Distance on L(U, U)
Inner products and triangularisation
The spectral radius
Normal maps
16. Quadratic forms and their relatives
Bilinear forms
Rank and signature
Positive definiteness
Antisymmetric bilinear forms
Further exercises.

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

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