For sophomore-level orjunior/senior-level first courses in linear algebra; assumes calculus as aprerequisite.
A thorough and accessibleintroduction to linear algebra.
The new 10thEdition of Linear Algebra with Applications continuesto encourage a challenging and broad understanding of the subject. For thisedition, Steven Leon―one of the leading figures in the use of technology forlinear algebra―is joined by new co-author Lisette de Pillis of Harvey MuddCollege, who brings her passion for teaching and solving real-world problems tothis revision.
Each chapter contains integratedworked examples, practical applications, computer exercises, and chapter tests. The important roles played by geometry and visualization in understandinglinear algebra are emphasized.
Cover Title Page Copyright Dedication Contents Preface Chapter 1: Matrices and Systems of Equations 1.1 Systems of Linear Equations 1.2 Row Echelon Form 1.3 Matrix Arithmetic 1.4 Matrix Algebra 1.5 Elementary Matrices 1.6 Partitioned Matrices Chapter 1 Exercises MATLAB Exercises Chapter Test A: True or False Chapter Test B Chapter 2: Determinants 2.1 The Determinant of a Matrix 2.2 Properties of Determinants 2.3 Additional Topics and Applications Chapter 2 Exercises MATLAB Exercises Chapter Test A True or False Chapter Test B Chapter 3: Vector Spaces 3.1 Definition and Examples 3.2 Subspaces 3.3 Linear Independence 3.4 Basis and Dimension 3.5 Change of Basis 3.6 Row Space and Column Space Chapter 3 Exercises MATLAB Exercises Chapter Test A True or False Chapter Test B Chapter 4: Linear Transformations 4.1 Definition and Examples 4.2 Matrix Representations of Linear Transformations 4.3 Similarity Chapter 4 Exercises MATLAB Exercises Chapter Test A True or False Chapter Test B Chapter 5: Orthogonality 5.1 The Scalar Product in Rn 5.2 Orthogonal Subspaces 5.3 Least Squares Problems 5.4 Inner Product Spaces 5.5 Orthonormal Sets 5.6 The Gram–Schmidt Orthogonalization Process 5.7 Orthogonal Polynomials Chapter 5 Exercises MATLAB Exercises Chapter Test A True or False Chapter Test B Chapter 6: Eigenvalues 6.1 Eigenvalues and Eigenvectors 6.2 Systems of Linear Differential Equations 6.3 Diagonalization 6.4 Hermitian Matrices 6.5 The Singular Value Decomposition 6.6 Quadratic Forms 6.7 Positive Definite Matrices 6.8 Nonnegative Matrices Chapter 6 Exercises MATLAB Exercises Chapter Test A True or False Chapter Test B Chapter 7: Numerical Linear Algebra 7.1 Floating-Point Numbers 7.2 Gaussian Elimination 7.3 Pivoting Strategies 7.4 Matrix Norms and Condition Numbers 7.5 Orthogonal Transformations 7.6 The Eigenvalue Problem 7.7 Least Squares Problems 7.8 Iterative Methods Chapter 7 Exercises MATLAB Exercises Chapter Test A True or False Chapter Test B Chapter 8: Canonical Forms 8.1 Nilpotent Operators 8.2 The Jordan Canonical Form Appendix: MATLAB Bibliography Answers to Selected Exercises Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
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