The continuing success of this text is due to its many current, relevant applications, "hands-on" approach and the emphasis it places on building student confidence and teaching flexibility. Linear dependence and linear independence are mentioned early and the 'Summing Up' Theorem reappears throughout the book to show students how seemingly disparate areas in matrix theory are closely linked. More than 300 examples and 1,700 exercises provide the practice students need, with more advanced, difficult theory included for optional use. The third edition has a more logical organization in the first chapter, presenting vectors and matrices before Gauss-Jordan elimination and covering the scalar product in conjunction with a new section on matrix product. Chapter 1 also has more challenging material added, to make the transition to later chapters more natural, such as new sections on homogeneous systems, elementary matrices and one-sided universes for non-square matrices. A more thorough proof that AB = det A det B in full generality and a more streamlined chapter on R2 and R3 are other new features of this edition. This book should be of interest to students taking linear algebra courses in departments of mathematics.
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1. Systems of Linear Equations and Matrices. 2. Determinants. 3. Vectors in R2 and R3. 4. Vector Spaces. 5. Linear Transformations. 6. Eigenvalues, Eigenvesors, And Canonical Forms. Appendix 1: Mathematical Induction. Appendix 2: Complex Numbers. Appendix 3: The Error in Numerical Computations and Computational Complexity. Appendix 4: Gaussian Elimination with Pivoting. Appendix 5: Using MATLAB.
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