Matrix Theory and Applications with MATLABDesigned 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 stresses insight, understanding, and applications. Among its most outstanding features is the integration of MATLAB throughout the text. Each chapter includes a MATLAB subsection that discusses the various commands used to do the computations in that section and offers code for the graphics and some algorithms used in the text. All of the material is presented from a matrix point of view with enough rigor for students to learn to compose arguments and proofs and adjust the material to cover other problems. The treatment includes optional subsections covering applications, and the final chapters move beyond basic matrix theory to discuss more advanced topics, such as decompositions, positive definite matrices, graphics, and topology. Filled with illustrations, examples, and exercises that reinforce understanding, Matrix Theory and Applications with MATLAB allows readers to experiment and visualize results in a way that no other text does. Its rigor, use of MATLAB, and focus on applications better prepares them to use the material in their future work and research, to extend the material, and perhaps obtain new results of their own. |
Contents
Review of Matrix Algebra | 1 |
Optional Dimension of Convex sets | 53 |
Similarity | 69 |
Matrix Calculus | 117 |
Normed Vector Spaces | 157 |
Unitary Similarity | 205 |
Singular Value Decomposition | 235 |
LU and QR Decompositions | 265 |
Properties of Eigenvalues and Eigenvectors | 291 |
Hermitian and Positive Definite Matrices | 309 |
Graphics and Topology | 331 |
MATLAB | 347 |
| 367 | |
| 370 | |
Common terms and phrases
a₁ backward multiplication calculation Chapter columns compute condition number converges Corollary corresponding eigenvectors defined diag diagonal matrix diagonalizable digits eigenvalues entries Euclidean n-space example Exercises factor Figure Find formula functions Gaussian elimination given graph grid view Hermitian matrix Householder matrix i-th induced matrix norm inner product Jordan blocks Jordan form k₂ least-squares solutions Lemma linearly independent lower triangular m x n main diagonal MATLAB n x n matrix nonsingular matrix nonzero Note obtain Optional orthogonal matrices orthogonal projection matrix orthonormal basis p₁ plot polynomial positive definite problem Proof properties Prove QR decomposition rank real numbers result row echelon form scalar sequence solve Ax span subspace Suppose symmetric Theorem triangular matrix type in help u₁ unitary matrix upper triangular vector norm vector space y₁ yields
References to this book
MATLAB 7: Eine Einführung Christoph W. Überhuber,Stefan Katzenbeisser,Dirk Praetorius No preview available - 2004 |