Solutions Manual for Lang’s Linear Algebra
Springer-Verlag New York Inc.
978-0-387-94760-0 (ISBN)
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.- §5. Schur’s Lemma.- §6. The Jordan Normal Form.- XII Convex Sets.- §4. The Krein-Milman Theorem.- APPENDIX Complex Numbers.
Zusatzinfo | XI, 200 p. |
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Verlagsort | New York, NY |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Analysis | |
Naturwissenschaften ► Physik / Astronomie | |
ISBN-10 | 0-387-94760-4 / 0387947604 |
ISBN-13 | 978-0-387-94760-0 / 9780387947600 |
Zustand | Neuware |
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