Solutions Manual for Lang’s Linear Algebra
The present volume contains all the exercises and their solutions of Lang's' Linear Algebra. Solving problems being an essential part of the learning process, my goal is to provide those learning and teaching linear algebra with a large number of worked out exercises. Lang's textbook...
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1996, 1996
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| Edition: | 1st ed. 1996 |
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- §5. Schur’s Lemma
- §6. The Jordan Normal Form
- XII Convex Sets
- §4. The Krein-Milman Theorem
- APPENDIX Complex Numbers
- I Vector Spaces
- §1. Definitions
- §2. Bases
- §4. Sums and Direct Sums
- II Matrices
- § 1. The Space of Matrices
- §2. Linear Equations
- §3. Multiplication of Matrices
- III Linear Mappings
- § 1. Mappings
- §2. Linear Mappings
- §3. The Kernel and Image of a Linear Map
- §4. Composition and Inverse of Linear Mappings
- §5. Geometric Applications
- IV Linear Maps and Matrices
- § 1. The Linear Map Associated with a Matrix
- §2. The Matrix Associated with a Linear Map
- §3. Bases, Matrices and Linear Map
- V Scalar Products and Orthogonality
- § 1. Scalar Products
- §2. Orthogonal bases, Positive Definite Case
- §3. Application to Linear Equations; the Rank
- §4. Bilinear Map and Matrices
- §5. General Orthogonal Bases
- §6. The Dual Space and Scalar Products
- §7. Quadratic Forms
- §8. Sylvester’s Theorem
- VI Determinants
- §2. Existence of Determinants
- §3. Additional Properties of Determinants
- §4. Cramer’s rule
- §5. Triangulation of a Matrix by Column Operations
- §6. Permutations
- §7. Expansion Formula and Uniqueness of Determinants
- §8. Inverse of a Matrix
- §9. The Rank of Matrix and Subdeterminants
- VII Symmetric, Hermitian and Unitary Operators
- §1. Symmetric Operators
- §2. Hermitian Operators
- §3. Unitary Operators
- VIII Eigenvectors and Eigenvalues
- §1. Eigenvectors and Eigenvalues
- §2. The Characteristic Polynomial
- §3. Eigenvalues and Eigenvectors of Symmetric Matrices
- §4. Diagonalization of a Symmetric Linear Map
- §5. The Hermitian Case
- IX Polynomials and Matrices
- §2. Polynomials of Matrices and Linear Maps
- X Triangulation of Matrices and Linear Maps
- §1. Existence of Triangulation
- §3. Diagonalization of Unitary Maps
- XI Polynomials and Primary Decomposition
- §1. The EuclideanAlgorithm
- §2. Greatest Common Divisor
- §3. Unique Factorization
- §4. Application to the Decomposition of a Vector Space