Linear Algebra For Dummies

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.

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