Linear Algebra with Applications
Autor Jeffrey Holten Limba Engleză Hardback – 14 dec 2016
Concepts and topics are frequently accompanied by applications to provide context and motivation. Because many students learn by example, Linear Algebra with Applications provides a large number of representative examples, over and above those used to introduce topics. The text also has over 2500 exercises, covering computational and conceptual topics over a range of difficulty levels.
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Specificații
ISBN-13: 9781464193347
ISBN-10: 1464193347
Pagini: 912
Dimensiuni: 203 x 254 x 25 mm
Greutate: 1.16 kg
Ediția:2
Editura: W H FREEMAN & CO LTD
ISBN-10: 1464193347
Pagini: 912
Dimensiuni: 203 x 254 x 25 mm
Greutate: 1.16 kg
Ediția:2
Editura: W H FREEMAN & CO LTD
Notă biografică
Jeffrey Holt
Cuprins
Preface
1. Systems of Linear Equations
1.1 Lines and Linear Equations
1.2 Linear Systems and Matrices
1.3 Applications of Linear Systems
1.4 Numerical Solutions
2. Euclidean Space
2.1 Vectors
2.2 Span
2.3 Linear Independence
3. Matrices
3.1 Linear Transformations
3.2 Matrix Algebra
3.3 Inverses
3.4 LU Factorization
3.5 Markov Chains
4. Subspaces
4.1 Introduction to Subspaces
4.2 Basis and Dimension
4.3 Row and Column Spaces
4.4 Change of Basis
5. Determinants
5.1 The Determinant Function
5.2 Properties of the Determinant
5.3 Applications of the Determinant
6. Eigenvalues and Eigenvectors
6.1 Eigenvalues and Eigenvectors
6.2 Diagonalization
6.3 Complex Eigenvalues and Eigenvectors
6.4 Systems of Differential Equations
6.5 Approximation Methods
7. Vector Spaces
7.1 Vector Spaces and Subspaces
7.2 Span and Linear Independence
7.3 Basis and Dimension
8. Orthogonality
8.1 Dot Products and Orthogonal Sets
8.2 Projection and the Gram-Schmidt Process
8.3 Diagonalizing Symmetric Matrices and QR Factorization
8.4 The Singular Value Decomposition
8.5 Least Squares Regression
9. Linear Transformations
9.1 Definition and Properties
9.2 Isomorphisms
9.3 The Matrix of a Linear Transformation
9.4 Similarity
10. Inner Product Spaces
10.1 Inner Products
10.2 The Gram-Schmidt Process Revisited
10.3 Applications of Inner Products
11. Additional Topics and Applications
11.1 Quadratic Forms
11.2 Positive Definite Matrices
11.3 Constrained Optimization
11.4 Complex Vector Spaces
11.5 Hermitian Matrices
Glossary
Answers to Selected Exercises
Index
1. Systems of Linear Equations
1.1 Lines and Linear Equations
1.2 Linear Systems and Matrices
1.3 Applications of Linear Systems
1.4 Numerical Solutions
2. Euclidean Space
2.1 Vectors
2.2 Span
2.3 Linear Independence
3. Matrices
3.1 Linear Transformations
3.2 Matrix Algebra
3.3 Inverses
3.4 LU Factorization
3.5 Markov Chains
4. Subspaces
4.1 Introduction to Subspaces
4.2 Basis and Dimension
4.3 Row and Column Spaces
4.4 Change of Basis
5. Determinants
5.1 The Determinant Function
5.2 Properties of the Determinant
5.3 Applications of the Determinant
6. Eigenvalues and Eigenvectors
6.1 Eigenvalues and Eigenvectors
6.2 Diagonalization
6.3 Complex Eigenvalues and Eigenvectors
6.4 Systems of Differential Equations
6.5 Approximation Methods
7. Vector Spaces
7.1 Vector Spaces and Subspaces
7.2 Span and Linear Independence
7.3 Basis and Dimension
8. Orthogonality
8.1 Dot Products and Orthogonal Sets
8.2 Projection and the Gram-Schmidt Process
8.3 Diagonalizing Symmetric Matrices and QR Factorization
8.4 The Singular Value Decomposition
8.5 Least Squares Regression
9. Linear Transformations
9.1 Definition and Properties
9.2 Isomorphisms
9.3 The Matrix of a Linear Transformation
9.4 Similarity
10. Inner Product Spaces
10.1 Inner Products
10.2 The Gram-Schmidt Process Revisited
10.3 Applications of Inner Products
11. Additional Topics and Applications
11.1 Quadratic Forms
11.2 Positive Definite Matrices
11.3 Constrained Optimization
11.4 Complex Vector Spaces
11.5 Hermitian Matrices
Glossary
Answers to Selected Exercises
Index