Format:
Online-Ressource
,
v.: digital
Edition:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics
ISBN:
9781461403388
Series Statement:
Universitext
Note:
Description based upon print version of record
,
""A Polynomial Approach to Linear Algebra""; ""Preface""; ""Preface to the Second Edition""; ""Contents""; ""Chapter 1: Algebraic Preliminaries""; ""1.1 Introduction""; ""1.2 Sets and Maps""; ""1.3 Groups""; ""1.4 Rings and Fields""; ""1.4.1 The Integers""; ""1.4.2 The Polynomial Ring""; ""1.4.3 Formal Power Series""; ""1.4.4 Rational Functions""; ""1.4.5 Proper Rational Functions""; ""1.4.6 Stable Rational Functions""; ""1.4.7 Truncated Laurent Series""; ""1.5 Modules""; ""1.6 Exercises""; ""1.7 Notes and Remarks""; ""Chapter 2: Vector Spaces""; ""2.1 Introduction""; ""2.2 Vector Spaces""
,
""2.3 Linear Combinations""""2.4 Subspaces""; ""2.5 Linear Dependence and Independence""; ""2.6 Subspaces and Bases""; ""2.7 Direct Sums""; ""2.8 Quotient Spaces""; ""2.9 Coordinates""; ""2.10 Change of Basis Transformations""; ""2.11 Lagrange Interpolation""; ""2.12 Taylor Expansion""; ""2.13 Exercises""; ""2.14 Notes and Remarks""; ""Chapter 3: Determinants""; ""3.1 Introduction""; ""3.2 Basic Properties""; ""3.3 Cramer's Rule""; ""3.4 The Sylvester Resultant""; ""3.5 Exercises""; ""3.6 Notes and Remarks""; ""Chapter 4: Linear Transformations""; ""4.1 Introduction""
,
""4.2 Linear Transformations""""4.3 Matrix Representations""; ""4.4 Linear Functionals and Duality""; ""4.5 The Adjoint Transformation""; ""4.6 Polynomial Module Structure on Vector Spaces""; ""4.7 Exercises""; ""4.8 Notes and Remarks""; ""Chapter 5: The Shift Operator""; ""5.1 Introduction""; ""5.2 Basic Properties""; ""5.3 Circulant Matrices""; ""5.4 Rational Models""; ""5.5 The Chinese Remainder Theorem and Interpolation""; ""5.5.1 Lagrange Interpolation Revisited""; ""5.5.2 Hermite Interpolation""; ""5.5.3 Newton Interpolation""; ""5.6 Duality""; ""5.7 Universality of Shifts""
,
""5.8 Exercises""""5.9 Notes and Remarks""; ""Chapter 6: Structure Theory of Linear Transformations""; ""6.1 Introduction""; ""6.2 Cyclic Transformations""; ""6.2.1 Canonical Forms for Cyclic Transformations""; ""6.3 The Invariant Factor Algorithm""; ""6.4 Noncyclic Transformations""; ""6.5 Diagonalization""; ""6.6 Exercises""; ""6.7 Notes and Remarks""; ""Chapter 7: Inner Product Spaces""; ""7.1 Introduction""; ""7.2 Geometry of Inner Product Spaces""; ""7.3 Operators in Inner Product Spaces""; ""7.3.1 The Adjoint Transformation""; ""7.3.2 Unitary Operators""
,
""7.3.3 Self-adjoint Operators""""7.3.4 The Minimax Principle""; ""7.3.5 The Cayley Transform""; ""7.3.6 Normal Operators""; ""7.3.7 Positive Operators""; ""7.3.8 Partial Isometries""; ""7.3.9 The Polar Decomposition""; ""7.4 Singular Vectors and Singular Values""; ""7.5 Unitary Embeddings""; ""7.6 Exercises""; ""7.7 Notes and Remarks""; ""Chapter 8: Tensor Products and Forms""; ""8.1 Introduction""; ""8.2 Basics""; ""8.2.1 Forms in Inner Product Spaces""; ""8.2.2 Sylvester's Law of Inertia""; ""8.3 Some Classes of Forms""; ""8.3.1 Hankel Forms""; ""8.3.2 Bezoutians""
,
""8.3.3 Representation of Bezoutians""
Additional Edition:
ISBN 9781461403371
Additional Edition:
Erscheint auch als Druck-Ausgabe Fuhrmann, Paul Abraham, 1937 - A polynomial approach to linear algebra New York, NY [u.a.] : Springer, 2012 ISBN 9781461403371
Language:
English
Subjects:
Mathematics
Keywords:
Lineare Algebra
;
Lineare Algebra
;
Lehrbuch
;
Lehrmittel
;
Lehrbuch
DOI:
10.1007/978-1-4614-0338-8
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Author information:
Fuhrmann, Paul Abraham 1937-
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