Linear algebra with applications /
- Ninth edition. Global edition.
- xvii, 520 pages : illustrations ; 25 cm
Includes bibliographical references and index.
PrefaceWhat's New in the Eighth Edition? Computer ExercisesOverview of TextSuggested Course OutlinesSupplementary MaterialsAcknowledgments 1. Matrices and Systems of Equations1.1 Systems of Linear Equations1.2 Row Echelon Form1.3 Matrix Arithmetic1.4 Matrix Algebra1.5 Elementary Matrices1.6 Partitioned Matrices Matlab Exercises Chapter Test A Chapter Test B 2. Determinants2.1 The Determinant of a Matrix2.2 Properties of Determinants2.3 Additional Topics and Applications Matlab Exercises Chapter Test A Chapter Test B 3. Vector Spaces3.1 Definition and Examples3.2 Subspaces3.3 Linear Independence3.4 Basis and Dimension3.5 Change of Basis3.6 Row Space and Column Space Matlab Exercises Chapter Test A Chapter Test B 4. Linear Transformations4.1 Definition and Examples4.2 Matrix Representations of Linear Transformations4.3 Similarity Matlab Exercises Chapter Test A Chapter Test B 5. Orthogonality5.1 The Scalar Product in Rn5.2 Orthogonal Subspaces5.3 Least Squares Problems5.4 Inner Product Spaces5.5 Orthonormal Sets5.6 The Gram-Schmidt Orthogonalization Process5.7 Orthogonal Polynomials Matlab Exercises Chapter Test A Chapter Test B 6. Eigenvalues6.1 Eigenvalues and Eigenvectors6.2 Systems of Linear Differential Equations6.3 Diagonalization6.4 Hermitian Matrices6.5 The Singular Value Decomposition6.6 Quadratic Forms6.7 Positive Definite Matrices6.8 Nonnegative Matrices Matlab Exercises Chapter Test A Chapter Test B 7. Numerical Linear Algebra7.1 Floating-Point Numbers7.2 Gaussian Elimination7.3 Pivoting Strategies7.4 Matrix Norms and Condition Numbers7.5 Orthogonal Transformations7.6 The Eigenvalue Problem7.7 Least Squares Problems Matlab Exercises Chapter Test A Chapter Test B Appendix: MATLABThe MATLAB Desktop DisplayBasic Data ElementsSubmatricesGenerating MatricesMatrix ArithmeticMATLAB FunctionsProgramming FeaturesM-filesRelational and Logical OperatorsColumnwise Array OperatorsGraphicsSymbolic ToolboxHelp FacilityConclusions BibliographyA. Linear Algebra and Matrix TheoryB. Applied and Numerical Linear AlgebraC. Books of Related Interest Answers to Selected Exercises.