The Oxford linear algebra for scientists : / Andre Lukas

Format:

Book

Author/Creator:

Lukas, Andre, author.

Series:

Oxford Academic

Oxford scholarship online

Language:

English

Subjects (All):

Algebra.

Science--Mathematics.

Science.

Algebras, Linear.

Physical Description:

1 online resource (433 pages)

Edition:

1st ed.

Place of Publication:

Oxford : Oxford University Press, 2022

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.

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*

ISBN:

0-19-188065-5

0-19-258347-6

OCLC:

1319212745