Author | Shakarchi, Rami. author |
---|---|
Title | Solutions Manual for Lang's Linear Algebra [electronic resource] / by Rami Shakarchi |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1996 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0755-9 |
Descript | XI, 200 p. online resource |
I Vector Spaces -- ยง1. Definitions -- ยง2. Bases -- ยง4. Sums and Direct Sums -- II Matrices -- ยง 1. The Space of Matrices -- ยง2. Linear Equations -- ยง3. Multiplication of Matrices -- III Linear Mappings -- ยง 1. Mappings -- ยง2. Linear Mappings -- ยง3. The Kernel and Image of a Linear Map -- ยง4. Composition and Inverse of Linear Mappings -- ยง5. Geometric Applications -- IV Linear Maps and Matrices -- ยง 1. The Linear Map Associated with a Matrix -- ยง2. The Matrix Associated with a Linear Map -- ยง3. Bases, Matrices and Linear Map -- V Scalar Products and Orthogonality -- ยง 1. Scalar Products -- ยง2. Orthogonal bases, Positive Definite Case -- ยง3. Application to Linear Equations; the Rank -- ยง4. Bilinear Map and Matrices -- ยง5. General Orthogonal Bases -- ยง6. The Dual Space and Scalar Products -- ยง7. Quadratic Forms -- ยง8. Sylvester's Theorem -- VI Determinants -- ยง2. Existence of Determinants -- ยง3. Additional Properties of Determinants -- ยง4. Cramer's rule -- ยง5. Triangulation of a Matrix by Column Operations -- ยง6. Permutations -- ยง7. Expansion Formula and Uniqueness of Determinants -- ยง8. Inverse of a Matrix -- ยง9. The Rank of Matrix and Subdeterminants -- VII Symmetric, Hermitian and Unitary Operators -- ยง1. Symmetric Operators -- ยง2. Hermitian Operators -- ยง3. Unitary Operators -- VIII Eigenvectors and Eigenvalues -- ยง1. Eigenvectors and Eigenvalues -- ยง2. The Characteristic Polynomial -- ยง3. Eigenvalues and Eigenvectors of Symmetric Matrices -- ยง4. Diagonalization of a Symmetric Linear Map -- ยง5. The Hermitian Case -- IX Polynomials and Matrices -- ยง2. Polynomials of Matrices and Linear Maps -- X Triangulation of Matrices and Linear Maps -- ยง1. Existence of Triangulation -- ยง3. Diagonalization of Unitary Maps -- XI Polynomials and Primary Decomposition -- ยง1. The Euclidean Algorithm -- ยง2. Greatest Common Divisor -- ยง3. Unique Factorization -- ยง4. Application to the Decomposition of a Vector Space -- ยง5. Schur's Lemma -- ยง6. The Jordan Normal Form -- XII Convex Sets -- ยง4. The Krein-Milman Theorem -- APPENDIX Complex Numbers