| Description |
1 online resource (433 pages) |
| Series |
Oxford scholarship online |
|
Oxford Academic
|
| Contents |
1 Linearity -- an informal introduction -- 2 Sets and functions -- 3 Groups -- 4 Fields -- 5 Coordinate vectors -- 6 Vector spaces -- 7 Elementary vector space properties -- 8 Vector subspaces -- 9 The dot product -- 10 Vector and triple product -- 11 Lines and planes -- 12 Introduction to linear maps -- 13 Matrices -- 14 The structure of linear maps -- 15 Linear maps in terms of matrices -- 16 Computing with matrices -- 17 Linear systems -- 18 Determinants -- 19 Basics of eigenvalues -- 20 Diagonalizing linear maps -- 21 The Jordan normal form* -- 22 Scalar products -- 23 Adjoint and unitary maps -- 24 Diagonalization -- again -- 25 Bi-linear and sesqui-linear forms* -- 26 The dual vector space* -- 27 Tensors* |
| Summary |
"This book provides a introduction into linear algebra which covers the mathematical set-up as well as applications to science. After the introductory material on sets, functions, groups and fields, the basic features of vector spaces are developed, including linear independence, bases, dimension, vector subspaces and linear maps. Practical methods for calculating with dot, cross and triple products are introduced early on. The theory of linear maps and their relation to matrices is developed in detail, culminating in the rank theorem. Algorithmic methods bases on row reduction and determinants are discussed an applied to computing the rank and the inverse of matrices and to solve systems of linear equations. Eigenvalues and eigenvectors and the application to diagonalising linear maps, as well as scalar products and unitary linear maps are covered in detail. Advanced topics included are the Jordon normal form, normal linear maps, the singular value decomposition, bi-linear and sesqui-linear forms, duality and tensors. The book also included short expositions of diverse scientific applications of linear algebra, including to internet search, classical mechanics, graph theory, cryptography, coding theory, data compression, special relativity, quantum mechanics and quantum computing"--Publisher's description |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from home page (Oxford Academic, viewed on June 30, 2023) |
| Subject |
Algebras, Linear.
|
|
Science -- Mathematics
|
|
Algebra.
|
|
algebra.
|
|
Algebras, Linear
|
|
Science -- Mathematics
|
| Form |
Electronic book
|
| ISBN |
9780191880650 |
|
0191880655 |
|
9780192583475 |
|
0192583476 |
|
