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Full Description
Offering the most geometric presentation available, Linear Algebra with Applications, Fifth Edition emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendly presentation with straightforward, lucid language to clarify and organize the techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum. Exercise sets are broad and varied and reflect the author's creativity and passion for this course. This revision reflects careful review and appropriate edits throughout, while preserving the order of topics of the previous edition.
Contents
1. Linear Equations1.1 Introduction to Linear Systems1.2 Matrices, Vectors, and Gauss-Jordan Elimination1.3 On the Solutions of Linear Systems; Matrix Algebra2. Linear Transformations2.1 Introduction to Linear Transformations and Their Inverses2.2 Linear Transformations in Geometry2.3 Matrix Products2.4 The Inverse of a Linear Transformation3. Subspaces of Rn and Their Dimensions3.1 Image and Kernel of a Linear Transformation3.2 Subspace of Rn; Bases and Linear Independence3.3 The Dimension of a Subspace of Rn3.4 Coordinates4. Linear Spaces4.1 Introduction to Linear Spaces4.2 Linear Transformations and Isomorphisms4.3 The Matrix of a Linear Transformation5. Orthogonality and Least Squares5.1 Orthogonal Projections and Orthonormal Bases5.2 Gram-Schmidt Process and QR Factorization5.3 Orthogonal Transformations and Orthogonal Matrices5.4 Least Squares and Data Fitting5.5 Inner Product Spaces6. Determinants6.1 Introduction to Determinants6.2 Properties of the Determinant6.3 Geometrical Interpretations of the Determinant; Cramer's Rule7. Eigenvalues and Eigenvectors7.1 Diagonalization 7.2 Finding the Eigenvalues of a Matrix7.3 Finding the Eigenvectors of a Matrix7.4 More on Dynamical Systems7.5 Complex Eigenvalues7.6 Stability8. Symmetric Matrices and Quadratic Forms8.1 Symmetric Matrices8.2 Quadratic Forms8.3 Singular Values9. Linear Differential Equations9.1 An Introduction to Continuous Dynamical Systems9.2 The Complex Case: Euler's Formula9.3 Linear Differential Operators and Linear Differential EquationsAppendix A. VectorsAppendix B: Techniques of ProofAnswers to Odd-numbered ExercisesSubject IndexName Index
