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Linear algebra : ideas and applications / Richard Penney.

By: Material type: TextTextPublication details: Hoboken, N.J. : John Wiley, c2008.Edition: 3rd edDescription: xvi, 480 p. ill. ; 25 cmISBN:
  • 9780470178843 (hbk.)
  • 0470178841 (hbk.)
Subject(s): DDC classification:
  • 512/.5 22 P4137
Contents:
Preface. Features of the Text. 1. Systems of Linear Equations. 1.1 The Vector Space of m x n Matrices. The Space Rn. Linear Combinations and Linear Dependence. What Is a Vector Space? Why Prove Anything? True-False Questions. Exercises. 1.1.1 Computer Projects. Exercises. 1.1.2 Applications to Graph Theory I. Self-Study Questions. Exercises. 1.2 Systems. Rank: The Maximum Number of Linearly Independent Equations. True-False Questions. Exercises. 1.2.1 Computer Projects. Exercises. 1.2.2 Applications to Circuit Theory. Self-Study Questions. Exercises. 1.3 Gaussian Elimination. Spanning in Polynomial Spaces. Computational Issues: Pivoting. True-False Questions. Exercises. Computational Issues: Flops. 1.3.1 Computer Projects. Exercises. 1.3.2 Applications to Traffic Flow. Self-Study Questions. Exercises. 1.4 Column Space and Nullspace. Subspaces. Subspaces of Functions. True-False Questions. Exercises. 1.4.1 Computer Projects. Exercises. 1.4.2 Applications to Predator-Prey Problems. Self-Study Questions. Exercises. Chapter Summary. 2. Linear Independence and Dimension. 2.1 The Test for Linear Independence. Bases for the Column Space. Testing Functions for Independence. True-False Questions. Exercises. 2.1.1 Computer Projects. 2.2 Dimension. True-False Questions. Exercises. 2.2.1 Computer Projects. Exercises. 2.2.2 Applications to Calculus. Self-Study Questions. Exercises. 2.2.3 Applications to Differential Equations. Self-Study Questions. Exercises. 2.2.4 Applications to the Harmonic Oscillator. Self-Study Questions. Exercises. 2.2.5 Computer Projects. Exercises. 2.3 Row Space and the Rank-Nullity Theorem. Bases for the Row Space. Rank-Nullity Theorem. Computational Issues: Computing Rank. True-False Questions. Exercises. 2.3.1 Computer Projects. Chapter Summary. 3. Linear Transformations. 3.1 The Linearity Properties. True-False Questions. Exercises. 3.1.1 Computer Projects. 3.1.2 Applications to Control Theory. Self-Study Questions. Exercises. 3.2 Matrix Multiplication (Composition). Partitioned Matrices. Computational Issues: Parallel Computing. True-False Questions. Exercises. 3.2.1 Computer Projects. 3.2.2 Applications to Graph Theory II. Self-Study Questions. Exercises. 3.3 Inverses. Computational Issues: Reduction vs. Inverses. True-False Questions. Exercises. Ill Conditioned Systems. 3.3.1 Computer Projects. Exercises. 3.3.2 Applications to Economics. Self-Study Questions. Exercises. 3.4 The LU Factorization. Exercises. 3.4.1 Computer Projects. Exercises. 3.5 The Matrix of a Linear Transformation. Coordinates. Application to Differential Equations. Isomorphism. Invertible Linear Transformations. True-False Questions. Exercises. 3.5.1 Computer Projects. Chapter Summary. 4. Determinants. 4.1 Definition of the Determinant. 4.1.1 The Rest of the Proofs. True-False Questions. Exercises. 4.1.2 Computer Projects. 4.2 Reduction and Determinants. Uniqueness of the Determinant. True-False Questions. Exercises. 4.2.1 Application to Volume. Self-Study Questions. Exercises. 4.3 A Formula for Inverses. Cramer’s Rule. True-False Questions. Exercises 273. Chapter Summary. 5. Eigenvectors and Eigenvalues. 5.1 Eigenvectors. True-False Questions. Exercises. 5.1.1 Computer Projects. 5.1.2 Application to Markov Processes. Exercises. 5.2 Diagonalization. Powers of Matrices. True-False Questions. Exercises. 5.2.1 Computer Projects. 5.2.2 Application to Systems of Differential Equations. Self-Study Questions. Exercises. 5.3 Complex Eigenvectors. Complex Vector Spaces. Exercises. 5.3.1 Computer Projects. Exercises. Chapter Summary. 6. Orthogonality. 6.1 The Scalar Product in Rn. Orthogonal/Orthonormal Bases and Coordinates. True-False Questions. Exercises. 6.1.1 Application to Statistics. Self-Study Questions. Exercises. 6.2 Projections: The Gram-Schmidt Process. The QR Decomposition 334. Uniqueness of the QR-factoriaition. True-False Questions. Exercises. 6.2.1 Computer Projects. Exercises. 6.3 Fourier Series: Scalar Product Spaces. Exercises. 6.3.1 Computer Projects. Exercises. 6.4 Orthogonal Matrices. Householder Matrices. True-False Questions. Exercises. 6.4.1 Computer Projects. Exercises. 6.5 Least Squares. Exercises. 6.5.1 Computer Projects. Exercises. 6.6 Quadratic Forms: Orthogonal Diagonalization. The Spectral Theorem. The Principal Axis Theorem. True-False Questions. Exercises. 6.6.1 Computer Projects. Exercises. 6.7 The Singular Value Decomposition (SVD). Application of the SVD to Least-Squares Problems. True-False Questions. Exercises. Computing the SVD Using Householder Matrices. Diagonalizing Symmetric Matrices Using Householder Matrices. 6.8 Hermitian Symmetric and Unitary Matrices. True-False Questions. Exercises. Chapter Summary. 7. Generalized Eigenvectors. 7.1 Generalized Eigenvectors. Exercises. 7.2 Chain Bases. Jordan Form. True-False Questions. Exercises. The Cayley-Hamilton Theorem. Chapter Summary. 8. Numerical Techniques. 8.1 Condition Number. Norms. Condition Number. Least Squares. Exercises. 8.2 Computing Eigenvalues. Iteration. The QR Method. Exercises. Chapter Summary. Answers and Hints. Index.
List(s) this item appears in: Mathematics | Computer_2022
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Books Books UE-Central Library 512.5 P4137 (Browse shelf(Opens below)) Available T1423

Includes index.

Preface.
Features of the Text.
1. Systems of Linear Equations.
1.1 The Vector Space of m x n Matrices.
The Space Rn.
Linear Combinations and Linear Dependence.
What Is a Vector Space?
Why Prove Anything?
True-False Questions.
Exercises.
1.1.1 Computer Projects.
Exercises.
1.1.2 Applications to Graph Theory I.
Self-Study Questions.
Exercises.
1.2 Systems.
Rank: The Maximum Number of Linearly Independent Equations.
True-False Questions.
Exercises.
1.2.1 Computer Projects.
Exercises.
1.2.2 Applications to Circuit Theory.
Self-Study Questions.
Exercises.
1.3 Gaussian Elimination.
Spanning in Polynomial Spaces.
Computational Issues: Pivoting.
True-False Questions.
Exercises.
Computational Issues: Flops.
1.3.1 Computer Projects.
Exercises.
1.3.2 Applications to Traffic Flow.
Self-Study Questions.
Exercises.
1.4 Column Space and Nullspace.
Subspaces.
Subspaces of Functions.
True-False Questions.
Exercises.
1.4.1 Computer Projects.
Exercises.
1.4.2 Applications to Predator-Prey Problems.
Self-Study Questions.
Exercises.
Chapter Summary.
2. Linear Independence and Dimension.
2.1 The Test for Linear Independence.
Bases for the Column Space.
Testing Functions for Independence.
True-False Questions.
Exercises.
2.1.1 Computer Projects.
2.2 Dimension.
True-False Questions.
Exercises.
2.2.1 Computer Projects.
Exercises.
2.2.2 Applications to Calculus.
Self-Study Questions.
Exercises.
2.2.3 Applications to Differential Equations.
Self-Study Questions.
Exercises.
2.2.4 Applications to the Harmonic Oscillator.
Self-Study Questions.
Exercises.
2.2.5 Computer Projects.
Exercises.
2.3 Row Space and the Rank-Nullity Theorem.
Bases for the Row Space.
Rank-Nullity Theorem.
Computational Issues: Computing Rank.
True-False Questions.
Exercises.
2.3.1 Computer Projects.
Chapter Summary.
3. Linear Transformations.
3.1 The Linearity Properties.
True-False Questions.
Exercises.
3.1.1 Computer Projects.
3.1.2 Applications to Control Theory.
Self-Study Questions.
Exercises.
3.2 Matrix Multiplication (Composition).
Partitioned Matrices.
Computational Issues: Parallel Computing.
True-False Questions.
Exercises.
3.2.1 Computer Projects.
3.2.2 Applications to Graph Theory II.
Self-Study Questions.
Exercises.
3.3 Inverses.
Computational Issues: Reduction vs. Inverses.
True-False Questions.
Exercises.
Ill Conditioned Systems.
3.3.1 Computer Projects.
Exercises.
3.3.2 Applications to Economics.
Self-Study Questions.
Exercises.
3.4 The LU Factorization.
Exercises.
3.4.1 Computer Projects.
Exercises.
3.5 The Matrix of a Linear Transformation.
Coordinates.
Application to Differential Equations.
Isomorphism.
Invertible Linear Transformations.
True-False Questions.
Exercises.
3.5.1 Computer Projects.
Chapter Summary.
4. Determinants.
4.1 Definition of the Determinant.
4.1.1 The Rest of the Proofs.
True-False Questions.
Exercises.
4.1.2 Computer Projects.
4.2 Reduction and Determinants.
Uniqueness of the Determinant.
True-False Questions.
Exercises.
4.2.1 Application to Volume.
Self-Study Questions.
Exercises.
4.3 A Formula for Inverses.
Cramer’s Rule.
True-False Questions.
Exercises 273.
Chapter Summary.
5. Eigenvectors and Eigenvalues.
5.1 Eigenvectors.
True-False Questions.
Exercises.
5.1.1 Computer Projects.
5.1.2 Application to Markov Processes.
Exercises.
5.2 Diagonalization.
Powers of Matrices.
True-False Questions.
Exercises.
5.2.1 Computer Projects.
5.2.2 Application to Systems of Differential Equations.
Self-Study Questions.
Exercises.
5.3 Complex Eigenvectors.
Complex Vector Spaces.
Exercises.
5.3.1 Computer Projects.
Exercises.
Chapter Summary.
6. Orthogonality.
6.1 The Scalar Product in Rn.
Orthogonal/Orthonormal Bases and Coordinates.
True-False Questions.
Exercises.
6.1.1 Application to Statistics.
Self-Study Questions.
Exercises.
6.2 Projections: The Gram-Schmidt Process.
The QR Decomposition 334.
Uniqueness of the QR-factoriaition.
True-False Questions.
Exercises.
6.2.1 Computer Projects.
Exercises.
6.3 Fourier Series: Scalar Product Spaces.
Exercises.
6.3.1 Computer Projects.
Exercises.
6.4 Orthogonal Matrices.
Householder Matrices.
True-False Questions.
Exercises.
6.4.1 Computer Projects.
Exercises.
6.5 Least Squares.
Exercises.
6.5.1 Computer Projects.
Exercises.
6.6 Quadratic Forms: Orthogonal Diagonalization.
The Spectral Theorem.
The Principal Axis Theorem.
True-False Questions.
Exercises.
6.6.1 Computer Projects.
Exercises.
6.7 The Singular Value Decomposition (SVD).
Application of the SVD to Least-Squares Problems.
True-False Questions.
Exercises.
Computing the SVD Using Householder Matrices.
Diagonalizing Symmetric Matrices Using Householder Matrices.
6.8 Hermitian Symmetric and Unitary Matrices.
True-False Questions.
Exercises.
Chapter Summary.
7. Generalized Eigenvectors.
7.1 Generalized Eigenvectors.
Exercises.
7.2 Chain Bases.
Jordan Form.
True-False Questions.
Exercises.
The Cayley-Hamilton Theorem.
Chapter Summary.
8. Numerical Techniques.
8.1 Condition Number.
Norms.
Condition Number.
Least Squares.
Exercises.
8.2 Computing Eigenvalues.
Iteration.
The QR Method.
Exercises.
Chapter Summary.
Answers and Hints.
Index.

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