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Full Description
An easy-to-follow guide to practical, real-world applications of linear algebra
Linear algebra is a branch of mathematics that uses matrices to solve systems of linear equations; it has applications in many disciplines, from sociology and game theory to computer programming, engineering, and business. Linear Algebra For Dummies maps to a typical, college-level linear algebra course, in which students first study matrices and matrix operations, then apply those fundamentals to abstract topics such as vector spaces, linear transformations, determinants, and, finally, eigenvalues and eigenvectors. It gives students theoretical and practical ways of approaching various types of problems, presenting the information in a way that allows readers to fully digest not just the how of solving linear algebraic problems, but also the why.
Contents
Introduction 1
Part I: Lining Up the Basics of Linear Algebra 7
Chapter 1: Putting a Name to Linear Algebra 9
Chapter 2: The Value of Involving Vectors 19
Chapter 3: Mastering Matrices and Matrix Algebra 41
Chapter 4: Getting Systematic with Systems of Equations 65
Part II: Relating Vectors and Linear Transformations 85
Chapter 5: Lining Up Linear Combinations 87
Chapter 6: Investigating the Matrix Equation Ax = b 105
Chapter 7: Homing In on Homogeneous Systems and Linear Independence 123
Chapter 8: Making Changes with Linear Transformations 147
Part III: Evaluating Determinants 173
Chapter 9: Keeping Things in Order with Permutations 175
Chapter 10: Evaluating Determinants 185
Chapter 11: Personalizing the Properties of Determinants 201
Chapter 12: Taking Advantage of Cramer's Rule 223
Part IV: Involving Vector Spaces 239
Chapter 13: Involving Vector Spaces 241
Chapter 14: Seeking Out Subspaces of Vector Spaces 255
Chapter 15: Scoring Big with Vector Space Bases 273
Chapter 16: Eyeing Eigenvalues and Eigenvectors 289
Part V: The Part of Tens 309
Chapter 17: Ten Real-World Applications Using Matrices 311
Chapter 18: Ten (Or So) Linear Algebra Processes You Can Do on Your Calculator 327
Chapter 19: Ten Mathematical Meanings of Greek Letters 339
Glossary 343
Index 351
