UID:
almahu_9947366122902882
Format:
1 online resource (225 p.)
ISBN:
1-282-28984-5
,
9786612289842
,
0-08-095590-8
Series Statement:
Mathematics in science and engineering ; v. 82-1
Content:
Multiparameter eigenvalue problems
Note:
Description based upon print version of record.
,
Front Cover; Multiparameter Eigenvalue Problems; Copyright Page; Contents; Preface; Contents of Volume II; PART I: PRELIMINARIES FROM LINEAR ALGEBRA; Chapter 1. Linear Spaces; 1.1 Introduction; 1.2 Linear Maps; 1 3 Composite and Induced Maps; 1.4 Direct Sums; 1.5 Linear Dependence and Dimension; 1.6 Dimensions of Kernel and Image; 1.7 Further Dimensional Results; 1.8 Topologies; 1.9 Connectedness; 1.10 Semilinear Maps; Chapter 2. Bilinear and Multilinear Functions; 2.1 Multilinear Functions; 2.2 Bilinear Functions; 2.3 Bilinear Functions on a Single Space; 2.4 Bilinear Forms
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2.5 Sesquilinear Functions2.6 Sesquilinear Forms and Endoniorphisms; 2.7 The Zeros of Hermitian Forms; 2.8 Pairs of Hermitian Forms; 2.9 Three Hermitian Forms; 2.10 General Remarks on the Range of a Set of Forms; Chapter 3. The Decomposition of Finite-Dimensional Endomorphisms; 3.1 Ascent and Descent; 3.2 The Case of Equal Ascent and Descent; 3.3 Eigensubspaces and Root Subspaces; 3.4 The Splitting Off of Root Subspaces; 3.5 The Finite-Dimensional Case; 3.6 Several Commuting Operators; 3.7 The Hermitian Case; 3.8 Orthogonality; 3.9 Some Modifications
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3.10 Reduction of Pairs of Hermitian FormsChapter 4. The Tensor Product of Linear Spaces; 4.1 Introduction; 4.2 The Definition by Means of Functionals; 4.3 Bases and Dimension; 4.4 The Real and Complex Cases; 4.5 Subspaces; 4.6 Induced Homomorphisms; 4.7 Exactness Properties; 4.8 Universal Property; 4.9 Bilinear Forms and Tensor Products; 4.10 Products of Sesquilinear Forms; Chapter 5. Tensor Products and Endomorphisms; 5.1 Introduction; 5.2 The Hermitian Case; 5.3 Eigenvalues and Ranks; 5.4 Decomposition; 5.5 The Kronecker Sum and Product; 5.6 Kronecker Sums and Eigenvalues
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5.7 Separation of Variables5.8 The Tensor Product of Identical Factors; 5.9 Induced Maps of Symmetry Subspaces; PART 2: MULTIPARAMETER PROBLEMS FOR MATRICES; Chapter 6. Simultaneous Equations in Linear Spaces; 6.1 Introduction; 6.2 Determinantal Maps; 6.3 Singular Determinantal Maps in the Case k = 2; 6.4 Rectangular Arrays; 6.5 Definiteness Requirements; 6.6 Solutions for Rectangular Arrays; 6.7 Nonformal Determinantal Properties; 6.8 Eigenvalues for a Rectangular Array; 6.9 Decomposition; Chapter 7. Simultaneous Eigenvalue Problems for Hermitian Matrices; 7.1 Introduction
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7.2 The First Definiteness Condition and Its Consequences7.3 Orthogonality of Eigenvectors; 7.4 Stronger Definiteness Conditions; 7.5 Splitting of Multiple Eigenvalues; 7.6 Decomposable Orthogonal Eigenvectors; 7.7 A Connectedness Property; 7.8 The Main Result on Positive Definiteness; 7.9 The Eigenvector Expansion; Chapter 8. The Singularity of Square Arrays; 8.1 Introduction; 8.2 Equivalent Singularity Conditions; 8.3 An Algebraic Lemma; 8.4 The Inductive Argument; 8.5 Singularity and Decomposable Tensors; 8.6 The Positive Definiteness Theorem Reproved; 8.7 Eigenvalues and Singularity
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Chapter 9. Arrays of Hermitian Forms
Additional Edition:
ISBN 0-12-065801-1
Language:
English
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