Rami Shakarchi

Solutions Manual for Lang's Linear Algebra (eBook, PDF)

• Format: PDF

Produktbeschreibung

This solutions manual for Lang's Undergraduate Analysis provides worked-out solutions for all problems in the text. They include enough detail so that a student can fill in the intervening details between any pair of steps.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 200
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461207559
• Artikelnr.: 44178740

Inhaltsangabe

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.