Author(s): G. C. Shephard
Series: University Mathematical Texts #32
Publisher: Oliver & Boyd
Year: 1966
Language: English
Pages: 200+viii
City: Edinburgh, London
Title
Preface
Contents
Summary of set theory and algebra
§ 0.1. Sets, Relations and Functions
§ 0.2. Groups, Rings and Fields
§ 0.3. Matrices
I. Vector spaces and subspaces
§ 1.1 The Definition of a Vector Space
§ 1.2. Subspaces
§ 1.3. Linear Dependence, Bases, Dimension
§ 1.4. Sums and Intersections of Subspaces
II. Linear transformations
§ 2.1. The Definition of a Linear Transformation
§ 2.2. Rank and Nullity
§ 2.3. Sums and Scalar Products of Linear Transformations
§ 2.4. Composition of Linear Transformations
§ 2.5. lnverses of Linear Transformations
§ 2.6. Invariant Subspaces
§ 2.7. Projections
§ 2.8. Characteristic Roots and Characteristic Vectors
§ 2.9. Reduction Theorems
III. Dual vector spaces
§ 3.1. Linear Functionals and Duality
§ 3.2. Annihilators
§ 3.3. The Dual of the Dual Space
§ 3.4. Dual Transformations
IV. Multilinear algebra
§ 4.1. Bilinear Functionals
§ 4.2. Tensor Products
§ 4.3. Antisymmetric Functionals
§ 4.4. Wedge Products
§ 4.5. Determinants and Characteristic Equation
V. Norms and inner products
§ 5.1. Norms
§ 5.2. Inner Products
§ 5.3. Orthogonal Complements
§ 5.4. Dual Spaces and Inner Products
§ 5.5. Adjoint Transformations
§ 5.6. Isometries
§ 5.7. Self-adjoint Transformations
VI. Coordinates and matrices
§ 6.1. Coordinates
§ 6.2. Linear Transformation in terms of Coordinates
§ 6.3. Change of Bases
§ 6.4. Canonical Forms for Matrices
Solutions to exercises
Index
