Linear Algebra For Dummies

Mary Jane Sterling is the author of numerous For Dummies books. She is a lecturer at Bradley University in Peoria, Illinois, where she has taught courses in algebra, calculus, and other mathematics topics for almost 30 years.

• Introduction 1Part I: Lining Up the Basics of Linear Algebra 7Chapter 1: Putting a Name to Linear Algebra 9Chapter 2: The Value of Involving Vectors 19Chapter 3: Mastering Matrices and Matrix Algebra 41Chapter 4: Getting Systematic with Systems of Equations 65Part II: Relating Vectors and Linear Transformations 85Chapter 5: Lining Up Linear Combinations 87Chapter 6: Investigating the Matrix Equation Ax = b 105Chapter 7: Homing In on Homogeneous Systems and Linear Independence 123Chapter 8: Making Changes with Linear Transformations 147Part III: Evaluating Determinants 173Chapter 9: Keeping Things in Order with Permutations 175Chapter 10: Evaluating Determinants 185Chapter 11: Personalizing the Properties of Determinants 201Chapter 12: Taking Advantage of Cramer's Rule 223Part IV: Involving Vector Spaces 239Chapter 13: Involving Vector Spaces 241Chapter 14: Seeking Out Subspaces of Vector Spaces 255Chapter 15: Scoring Big with Vector Space Bases 273Chapter 16: Eyeing Eigenvalues and Eigenvectors 289Part V: The Part of Tens 309Chapter 17: Ten Real-World Applications Using Matrices 311Chapter 18: Ten (Or So) Linear Algebra Processes You Can Do on Your Calculator 327Chapter 19: Ten Mathematical Meanings of Greek Letters 339Glossary 343Index 351