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Book Categories |
Ch. 1 | Vectors | 1 |
1.1 | Vectors and Matrices in Engineering and Mathematics; n-Space | 1 |
1.2 | Dot Product and Orthogonality | 15 |
1.3 | Vector Equations of Lines and Planes | 29 |
Ch. 2 | Systems of Linear Equations | 39 |
2.1 | Introduction to Systems of Linear Equations | 39 |
2.2 | Solving Linear Systems by Row Reduction | 48 |
2.3 | Applications of Linear Systems | 63 |
Ch. 3 | Matrices and Matrix Algebra | 79 |
3.1 | Operations on Matrices | 79 |
3.2 | Inverses; Algebraic Properties of Matrices | 94 |
3.3 | Elementary Matrices; A Method for Finding A[superscript -1] | 109 |
3.4 | Subspaces and Linear Independence | 123 |
3.5 | The Geometry of Linear Systems | 135 |
3.6 | Matrices with Special Forms | 143 |
3.7 | Matrix Factorizations; LU-Decomposition | 154 |
3.8 | Partitioned Matrices and Parallel Processing | 166 |
Ch. 4 | Determinants | 175 |
4.1 | Determinants; Cofactor Expansion | 175 |
4.2 | Properties of Determinants | 184 |
4.3 | Cramer's Rule; Formula for A[superscript -1]: Applications of Determinants | 196 |
4.4 | A First Look at Eigenvalues and Eigenvectors | 210 |
Ch. 5 | Matrix Models | 225 |
5.1 | Dynamical Systems and Markov Chains | 225 |
5.2 | Leontief Input-Output Models | 235 |
5.3 | Gauss-Seidel and Jacobi Iteration; Sparse Linear Systems | 241 |
5.4 | The Power Method; Application to Internet Search Engines | 249 |
Ch. 6 | Linear Transformations | 265 |
6.1 | Matrices as Transformations | 265 |
6.2 | Geometry of Linear Operators | 280 |
6.3 | Kernel and Range | 296 |
6.4 | Composition and Invertibility of Linear Transformations | 305 |
6.5 | Computer Graphics | 318 |
Ch. 7 | Dimension and Structure | 329 |
7.1 | Basis and Dimension | 329 |
7.2 | Properties of Bases | 335 |
7.3 | The Fundamental Spaces of a Matrix | 342 |
7.4 | The Dimension Theorem and Its Implications | 352 |
7.5 | The Rank Theorem and Its Implications | 360 |
7.6 | The Pivot Theorem and Its Implications | 370 |
7.7 | The Projection Theorem and Its Implications | 379 |
7.8 | Best Approximation and Least Squares | 393 |
7.9 | Orthonormal Bases and the Gram-Schmidt Process | 406 |
7.10 | QR-Decomposition; Householder Transformations | 417 |
7.11 | Coordinates with Respect to a Basis | 426 |
Ch. 8 | Diagonalization | 443 |
8.1 | Matrix Representations of Linear Transformations | 443 |
8.2 | Similarity and Diagonalizability | 456 |
8.3 | Orthogonal Diagonalizability; Functions of a Matrix | 468 |
8.4 | Quadratic Forms | 481 |
8.5 | Application of Quadratic Forms to Optimization | 495 |
8.6 | Singular Value Decomposition | 502 |
8.7 | The Pseudoinverse | 518 |
8.8 | Complex Eigenvalues and Eigenvectors | 525 |
8.9 | Hermitian, Unitary, and Normal Matrices | 535 |
8.10 | Systems of Differential Equations | 542 |
Ch. 9 | General Vector Spaces | 555 |
9.1 | Vector Space Axioms | 555 |
9.2 | Inner Product Spaces; Fourier Series | 569 |
9.3 | General Linear Transformations; Isomorphism | 582 |
App. A | How to Read Theorems | |
App. B | Complex Numbers | |
Answers to Odd-Numbered Exercises | ||
Photo Credits | ||
Index |
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Add Contemporary Linear Algebra, From one of the premier authors in higher education comes a new linear algebra textbook that fosters mathematical thinking, problem-solving abilities, and exposure to real-world applications. Without sacrificing mathematical precision, Anton and Busby foc, Contemporary Linear Algebra to the inventory that you are selling on WonderClubX
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Add Contemporary Linear Algebra, From one of the premier authors in higher education comes a new linear algebra textbook that fosters mathematical thinking, problem-solving abilities, and exposure to real-world applications. Without sacrificing mathematical precision, Anton and Busby foc, Contemporary Linear Algebra to your collection on WonderClub |