Linear Algebra for Engineers and Scientists / Edition 1

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This short book integrates the use of MATLAB in a unique, innovative way. Linear transformations are integrated throughout the book. The book uses MATLAB as the chosen computational software. It may be used without the need form machine computation, although exposure to some use of MATLAB is recommended. Worked examples illustrating every important concept or main point. At the end of each example the reader is asked to work one (or more) routine exercises which are of the same type. Although the book has been developed in the context of engineering and computer science, it is also suitable for other audiences.

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Table of Contents

(NOTE: A (historic) profile and introduction are keynotes to each chapter.)

1. Linear Systems.

Solving Linear Systems. Echelon Forms, Rank. Applications.

2. Matrices.

Matrix Algebra. Inverses. LU-Factorization. Applications.

3. Vectors.

Spaces of Vectors. Linear Independence, Bases, Dimension. Null Space, Column Space, Row Space. Linear Transformations on Rn.

4. Orthogonality.

Dot Product, Norm. Orthogonal Sets, Orthogonal Matrices. Orthogonal Subspaces, Projections, Bases. Applications.

5. Determinants.

Definition and Computation. Inverses and Products.

6. Eigenvalue Problems.

Eigenvalues and Eigenvectors. Diagonalization. Applied Eignevalue Problems. Markov Chains. Systems of Linear Differential Equations.

7. Vector Spaces.

Vector Spaces and Subspaces. Linear Independence, Basis, Dimension. Coordinates, Linear Transformations.

8. Complex Numbers.

Algebraic Theory. Geometric Theory. Polar Form. Extraction of Roots, Polynomials. Linear Algebra: The Complex Case.

9. Linear Programming.

Standard Forms, Geometrical Methods. The Simplex Algorithm. Duality. Mixed Constraints.

Appendix A: MATLAB.

Appendix B: TOOLBOX.

Answers to Selected Odd-Numbered Exercises


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