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Book Categories |
| 1 | Review of Matrix Algebra | 1 |
| 1.1 | Matrices, Systems of Linear Equations, Determinants | 1 |
| 1.1.1 | Matrix Algebra | 3 |
| 1.1.2 | Systems of Linear Equations | 12 |
| 1.1.3 | Determinant | 15 |
| 1.1.4 | Optional (Ranking) | 20 |
| 1.1.5 | MATLAB (Solving Ax = b) | 22 |
| 2 | Introduction to Vector Spaces | 29 |
| 2.1 | Vector Spaces | 29 |
| 2.1.1 | Optional (Geometrical Description of the Solutions to Ax = b) | 39 |
| 2.1.2 | MATLAB (Graphics) | 40 |
| 2.2 | Dimension | 43 |
| 2.2.1 | Optional (Dimension of Convex sets) | 53 |
| 2.3 | Linear Transformations | 58 |
| 2.3.1 | Optional (Graphics of Polygonal Shapes) | 67 |
| 2.3.2 | MATLAB (Codes, including Picture of the Singular Matrices in Matrix Space) | 69 |
| 3 | Similarity | 75 |
| 3.1 | Nonsingular Matrices | 76 |
| 3.1.1 | Optional (Interpolation and Pictures) | 82 |
| 3.1.2 | MATLAB (Polyfit and Polyval) | 84 |
| 3.2 | Diagonalization | 87 |
| 3.2.1 | Optional (Buckling Beam) | 93 |
| 3.2.2 | MATLAB (Eig and [P, D]) | 96 |
| 3.3 | Conditions for Diagonalization | 99 |
| 3.3.1 | Optional (Picture of Multiple Eigenvalue Matrices in Matrix Space) | 105 |
| 3.3.2 | MATLAB (Code for Picture) | 106 |
| 3.4 | Jordan Forms | 108 |
| 3.4.1 | Optional (Numerical Problems in Finding the Jordan Form) | 113 |
| 3.4.2 | MATLAB ([P, D] and Defective A) | 114 |
| 4 | Matrix Calculus | 117 |
| 4.1 | Calculus of Matrices | 117 |
| 4.1.1 | Optional (Modeling Spring-Mass Problems) | 124 |
| 4.1.2 | MATLAB (Code for Graph of Function) | 126 |
| 4.2 | Difference Equations | 128 |
| 4.2.1 | Optional (Long-Run Prediction) | 135 |
| 4.2.2 | MATLAB (Code for Viewing Solution to Difference Equations; Handling Large Matrices) | 137 |
| 4.3 | Differential Equations | 142 |
| 4.3.1 | Optional (Modeling Motions of a Building) | 151 |
| 4.3.2 | MATLAB (Code for Viewing Solutions of Differential Equations Using expm) | 152 |
| 5 | Normed Vector Spaces | 157 |
| 5.1 | Vector Norms | 157 |
| 5.1.1 | Optional (Evaluating Models) | 162 |
| 5.1.2 | MATLAB (Vector Norms) | 164 |
| 5.2 | Induced Matrix Norms | 166 |
| 5.2.1 | Optional (Error in Solving Ax = b) | 173 |
| 5.2.2 | MATLAB (Matrix Norms and Condition Numbers) | 176 |
| 5.3 | Some Special Norms | 180 |
| 5.3.1 | Optional (Splitting Techniques) | 185 |
| 5.3.2 | MATLAB (Code for Iterative Solutions) | 187 |
| 5.4 | Inner Product Norms and Orthogonality | 191 |
| 5.4.1 | Optional (Closest Matrix from Symmetric Matrices) | 200 |
| 5.4.2 | MATLAB (Orth and the Projection Matrix) | 200 |
| 6 | Unitary Similarity | 205 |
| 6.1 | Unitary Matrices | 205 |
| 6.1.1 | Optional (Symmetry) | 213 |
| 6.1.2 | MATLAB (Code for Picture of Orthogonal Matrices in 2 [times] 2 Matrix Space) | 215 |
| 6.2 | Schur Decompositions | 219 |
| 6.2.1 | Optional (Motion in Principal Axes) | 228 |
| 6.2.2 | MATLAB (Schur) | 231 |
| 7 | Singular Value Decomposition | 235 |
| 7.1 | Singular Value Decomposition Theorem | 236 |
| 7.1.1 | Optional (Physical Problems involving Least-Squares Solutions) | 245 |
| 7.1.2 | MATLAB (Least-Squares Solutions to Ax = b) | 248 |
| 7.2 | Applications of the SVD Theorem | 252 |
| 7.2.1 | MATLAB (pinv, null, orth, and rank) | 260 |
| 8 | LU and QR Decompositions | 265 |
| 8.1 | The LU Decomposition | 265 |
| 8.1.1 | Optional (Iterative Improvement in Solving Ax = b) | 272 |
| 8.1.2 | MATLAB (lu, [L, U] and [L, U, F]) | 273 |
| 8.2 | The QR Decomposition | 275 |
| 8.2.1 | Optional (QR Algorithm) | 283 |
| 8.2.2 | MATLAB (Ax = b, QR, Householder, and Givens) | 285 |
| 9 | Properties of Eigenvalues and Eigenvectors | 291 |
| 9.1 | Continuity of Eigenvalues and Eigenvectors | 291 |
| 9.1.1 | Optional (Eigenvectors and Multiple Eigenvalues) | 297 |
| 9.2 | Perturbation of Eigenvalues and Eigenvectors | 299 |
| 9.2.1 | Optional (Pictures of Eigenvalue and Eigenvector Sensitivity) | 304 |
| 9.2.2 | MATLAB (Condeig) | 306 |
| 10 | Hermitian and Positive Definite Matrices | 309 |
| 10.1 | Positive Definite Matrices | 309 |
| 10.1.1 | Optional (Solving the Motion of a Building Problem) | 315 |
| 10.1.2 | MATLAB (Code for Computing P) | 318 |
| 10.2 | Special Eigenvalue Results on Hermitian Matrices | 320 |
| 10.2.1 | Optional (Optimization) | 326 |
| 11 | Graphics and Topology | 331 |
| 11.1 | Two Projection Matrices | 331 |
| 11.1.1 | Optional (Drawing Pictures Using Projection Maps) | 337 |
| 11.2 | Manifolds and Topological Sets | 340 |
| 11.2.1 | Optional (Rank k Matrices) | 344 |
| Appendix A | MATLAB | 346 |
| Answers to Selected Exercises | 350 | |
| Bibliography | 365 |
| Price | Condition | Delivery | Seller | Action |
| $110.55 | Digital |
| WonderClub |
SOCRATES PINTO
reviewed Matrix Theory and Applications with MATLAB on August 03, 2013
Matrix Theory and Applications with MATLAB
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Add Matrix Theory and Applications with MATLAB, Designed for use in a second course on linear algebra, Matrix Theory and Applications with MATLAB covers the basics of the subject-from a review of matrix algebra through vector spaces to matrix calculus and unitary similarity-in a presentation that stres, Matrix Theory and Applications with MATLAB to the inventory that you are selling on WonderClubX
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Add Matrix Theory and Applications with MATLAB, Designed for use in a second course on linear algebra, Matrix Theory and Applications with MATLAB covers the basics of the subject-from a review of matrix algebra through vector spaces to matrix calculus and unitary similarity-in a presentation that stres, Matrix Theory and Applications with MATLAB to your collection on WonderClub |