Linear Algebra : Ideas and Applications

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Preface. Features of the Text. 1. Systems of Linear Equations. 1.1 The Vector Space of mxn Matrices 1.1.1 Computer Projects.

1.1.2 Applications to Graph Theory 1. 1.2 Systems. 1.2.1 Computer Projects.

1.2.2 Applications to Circuit Theory. 1.3 Gaussian Elimination. 1.3.1 Computer Projects.

1.3.2 Applications to Traffic Flow. 1.4 Column Space and Nullspace. 1.4 1 Computer Projects. 1.

4.2 Applications to Predator-Prey Problems. 2. Linear Independence and Dimension. 2.1 The Test for Linear Independence. 2.1.

1 Computer Projects. 2.2 Dimension. 2.2.1 Computer Projects. 2.2.

2 Applications to Calculus. 2.2.3 Applications to Differential Equations. 2.2.4 Applications to the Harmonic Oscillator. 2.

2.5 Computer Projects. 2.3 Row Space and the Rank-Nullity Theorem. 2.3.1 Computer Projects. 3.

Linear Transformations. 3.1 The Linearity Properties. 3.1.1 Computer Projects. 3.1.

2 Applications to Control Theory. 3.2 Matrix Multiplication (Composition). 3.2.1 Computer Projects. 3.2.

2 Applications to Graph Theory II. 3.3 Inverses. 3.3.1 Computer Projects. 3.3.

2 Applications to Economics. 3.4 The LU Factorization. 3.4.1 Computer Projects. 3.5 The Matrix of Linear Transformation.

3.5.1 Computer Projects. 4. Determinants. 4.1 Definition of the Determinants. 4.

1.1 The Rest of the Proofs. 4.1.2 Computer Projects. 4.2 Reduction and Determinants. 4.

2.1 Application to Volume. 4.3 A Formula for Inverses. 5. Eigenvectors and Eigenvalues. 5.1 Eigenvectors.

5.1.1 Computer Projects. 5.1.2 Application to Markov Processes. 5.2 Diagonalization.

5.2.1 Computer Projects. 5.2.2 Applications to Systems of Differential Equations. 5.3 Complex Eigenvectors.

5.3.1 Computer Projects. 6. Orthogonality. 6.1 The Scalar Product in R n . 6.

1.1 Application to Statistics. 6.2 Projections: The Gram-Schmidt Process. 6.2.1 Computer Projects. 6.

3 Fourier Series: Scalar Product Spaces. 6.3.1 Computer Projects. 6.4 Orthogonal Matrices. 6.5 Least Squares.

6.5.1 Computer Projects. 6.6 Quadratic Forms: Orthogonal Diagonalization. 6.6.1 Computer Projects.

6.7 The Singular Value Decomposition. Appendix: Answers and Hints. Glossary. Index.

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