A Guide to Advanced Linear Algebra /
| Основен автор: | Weintraub, Steven H. |
|---|---|
| Формат: | Електронна книга |
| Език: | English |
| Публикувано: |
Cambridge :
Cambridge University Press,
2012.
|
| Серия: |
Dolciani mathematical expositions.
|
| Предмети: | |
| Онлайн достъп: |
http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450279 |
| Подобни документи: |
Print version::
Guide to Advanced Linear Algebra. |
Съдържание:
- ""Front cover ""; ""copyright page ""; ""title page ""; ""Preface""; ""Contents""; ""1 Vector spaces and linear transformations""; ""1.1 Basic definitions and examples""; ""1.2 Basis and dimension""; ""1.3 Dimension counting and applications""; ""1.4 Subspaces and direct sum decompositions""; ""1.5 Affine subspaces and quotient spaces""; ""1.6 Dual spaces""; "" 2 Coordinates""; ""2.1 Coordinates for vectors""; ""2.2 Matrices for linear transformations""; ""2.3 Change of basis""; ""2.4 The matrix of the dual""; ""3 Determinants""; ""3.1 The geometry of volumes""
- ""3.2 Existence and uniqueness of determinants""""3.3 Further properties""; ""3.4 Integrality""; ""3.5 Orientation""; ""3.6 Hilbert matrices""; ""4 The structure of alinear transformation I""; ""4.1 Eigenvalues, eigenvectors, and generalized eigenvectors""; ""4.2 Some structural results""; ""4.3 Diagonalizability""; ""4.4 An application todifferential equations""; ""5 The structure of a linear transformation II""; ""5.1 Annihilating, minimum, and characteristic polynomials""; ""5.2 Invariant subspaces and quotient spaces""
- ""5.3 The relationship between the characteristic and minimum polynomials""""5.4 Invariant subspaces and invariant complements""; ""5.5 Rational canonical form""; ""5.6 Jordan canonical form""; ""5.7 An algorithm for Jordan canonical form and Jordan basis""; ""5.8 Field extensions""; ""5.9 More than one linear transformation""; ""6 Bilinear, sesquilinear, and quadratic forms""; ""6.1 Basic definitions and results""; ""6.2 Characterization and classification theorems""; ""6.3 The adjoint of a linear transformation""; ""7 Real and complex inner product spaces""; ""7.1 Basic definitions""
- ""7.2 The Gram-Schmidt process""""7.3 Adjoints, normal linear transformations, and the spectral theorem""; ""7.4 Examples""; ""7.5 The singular value decomposition""; ""8 Matrix groups as Lie groups""; ""8.1 Definition and first examples""; ""8.2 Isometry groups of forms""; ""Appendix A: Polynomials""; ""A.1 Basic properties""; ""A.2 Unique factorization""; ""A.3 Polynomials as expressions and polynomials as functions""; ""Appendix B: Modules over principal ideal domains""; ""B.1 Definitions and structure theorems""; ""B.2 Derivation of canonical forms""; ""Bibliography""; ""Index""