Introduction to Matrices, Sets and Groups for Science Students

Name: Introduction to Matrices, Sets and Groups for Science Students
Brand: Dover Publications
Price: 18.99 EUR
Availability: OnlineOnly

G. Stephenson(Autor*in)

Dover Publications (Verlag)

Erschienen am 14. Januar 2016

203 Seiten

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978-0-486-80916-8 (ISBN)

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Inhalt

Cover
Title page
Copyright
Contents
Preface
1. Sets, Mappings and Transformations
1.1 Introduction
1.2 Sets
1.3 Venn diagrams
1.4 Mappings
1.5 Linear transformations and matrices
1.6 Occurrence and uses of matrices
1.7 Operations with sets
1.8 Set algebra
1.9 Some elementary applications of set theory
Problems 1
2. Matrix Algebra
2.1 Laws of matrix algebra
2.2 Partitioning of matrices
2.3 Some special types of matrices
Problems 2
3. The Inverse and Related Matrices
3.1 Introduction
3.2 The adjoint matrix
3.3 The inverse matrix
3.4 Some properties of the inverse matrix
3.5 Evaluation of the inverse matrix by partitioning
3.6 Orthogonal matrices and orthogonal transformations
3.7 Unitary matrices
Problems 3
4. Systems of Linear Algebraic Equations
4.1 Introduction
4.2 Non-homogeneous equations
4.3 Homogeneous equations
4.4 Ill-conditioned equations
Problems 4
5. Eigenvalues and Eigenvectors
5.1 Introduction
5.2 Eigenvalues and eigenvectors
5.3 Some properties of eigenvalues
5.4 Repeated eigenvalues
5.5 Orthogonal properties of eigenvectors
5.6 Real symmetric matrices
5.7 Hermitian matrices
5.8 Non-homogeneous equations
Problems 5
6. Diagonalisation of Matrices
6.1 Introduction
6.2 Similar matrices
6.3 Diagonalisation of a matrix whose eigenvalues are all different
6.4 Matrices with repeated eigenvalues
6.5 Diagonalisation of real symmetric matrices
6.6 Diagonalisation of Hermitian matrices
6.7 Bilinear and quadratic forms
6.8 Lagrange's reduction of a quadratic form
6.9 Matrix diagonalisation of a real quadratic form
6.10 Hermitian forms
6.11 Simultaneous diagonalisation of two quadratic forms
Problems 6
7. Functions of Matrices
7.1 Introduction
7.2 Cayley-Hamilton theorem
7.3 Powers of matrices
7.4 Some matrix series
7.5 Differentiation and integration of matrices
Problems 7
8. Group Theory
8.1 Introduction
8.2 Group axioms
8.3 Examples of groups
8.4 Cyclic groups
8.5 Group tables
8.6 Isomorphic groups
8.7 Permutations: the symmetric group
8.8 Cayley's theorem
8.9 Subgroups and cosets
8.10 Some remarks on representations
Problems 8
Further Reading
Answers to Problems
Index

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