This book explores linear algebra using an approach that introduces abstract concepts only as they are needed to understand the computations. No new concepts are introduced without first justifying their importance and relationship to something that is already in the readers' sphere of experience, allowing readers to see immediately why each concept is necessary. This approach ensures that the relation between theory and application is clear and immediate.
This book explores linear algebra using an approach that introduces abstract concepts only as they are needed to understand the computations. No new concepts are introduced without first justifying their importance and relationship to something that is already in the readers' sphere of experience, allowing readers to see immediately why each concept is necessary. This approach ensures that the relation between theory and application is clear and immediate.
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Für höhere Schule und Studium
ISBN-13
978-0-471-66131-3 (9780471661313)
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Schweitzer Klassifikation
RICHARD C. PENNEY, PhD, is Professor in the Department of Mathematics and Director of the Mathematics/Statistics Actuarial Science Program at Purdue University, Lafayette, Indiana. He has authored several journal articles and has received several major teaching awards.
RICHARD C. PENNEY, PhD, is Professor in the Department of Mathematics and Director of the Mathematics/Statistics Actuarial Science Program at Purdue University, Lafayette, Indiana. He has authored several journal articles and has received several major teaching awards.
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 of Linear Equations. 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 Linear Transformations. 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 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 A. Answers and Hints. Glossary. Index.
