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• About the Author
• Dedication
• Author’s Acknowledgments
• Contents at a Glance
• Table of Contents
• Introduction
• About This Book
• Conventions Used in This Book
• What You’re Not to Read
• Foolish Assumptions
• How This Book Is Organized
• Icons Used in This Book
• Where to Go from Here
• Part I: Lining Up the Basics of Linear Algebra
• Chapter 1: Putting a Name to Linear Algebra
• Solving Systems of Equations in Every Which Way but Loose
• Matchmaking by Arranging Data in Matrices
• Valuating Vector Spaces
• Determining Values with Determinants
• Zeroing In on Eigenvalues and Eigenvectors
• Chapter 2: The Value of Involving Vectors
• Describing Vectors in the Plane
• Defining the Algebraic and Geometric Properties of Vectors
• Managing a Vector’s Magnitude
• Chapter 3: Mastering Matrices and Matrix Algebra
• Getting Down and Dirty with Matrix Basics
• Putting Matrix Operations on the Schedule
• Putting Labels to the Types of Matrices
• Connecting It All with Matrix Algebra
• Investigating the Inverse of a Matrix
• Chapter 4: Getting Systematic with Systems of Equations
• Investigating Solutions for Systems
• Dealing with Inconsistent Systems and No Solution
• Solving Systems Algebraically
• Revisiting Systems of Equations Using Matrices
• Part II: Relating Vectors and Linear Transformations
• Chapter 5: Lining Up Linear Combinations
• Defining Linear Combinations of Vectors
• Getting Your Attention with Span
• Chapter 6: Investigating the Matrix Equation AX=b
• Working Through Matrix-Vector Products
• Confirming the Existence of a Solution or Solutions
• Chapter 7: Homing In on Homogeneous Systems and Linear Independence
• Seeking Solutions of Homogeneous Systems
• Delving Into Linear Independence
• Connecting Everything to Basis
• Chapter 8: Making Changes with Linear Transformations
• Formulating Linear Transformations
• Proposing Properties of Linear Transformations
• Writing the Matrix of a Linear Transformation
• Determining the Kernel and Range of a Linear Transformation
• Part III: Evaluating Determinants
• Chapter 9: Keeping Things in Order with Permutations
• Computing and Investigating Permutations
• Involving Inversions in the Counting
• Chapter 10: Determining Values of Determinants
• Evaluating the Determinants of 2 × 2 Matrices
• Using Determinants with Area and Volume
• Chapter 11: Personalizing the Properties of Determinants
• Transposing and Inverting Determinants
• Interchanging Rows or Columns
• Zeroing In on Zero Determinants
• Manipulating Matrices by Multiplying and Combining
• Taking on Upper or Lower Triangular Matrices
• Determinants of Matrix Products
• Chapter 12: Taking Advantage of Cramer’s Rule
• Inviting Inverses to the Party with Determined Determinants
• Solving Systems Using Cramer’s Rule
• Recognizing and Dealing with a Nonanswer
• Making a Case for Calculators and Computer Programs
• Part IV: Involving Vector Spaces
• Chapter 13: Promoting the Properties of Vector Spaces
• Delving into the Vector Space
• Describing the Two Operations
• Singling Out the Specifics of Vector Space Properties
• Chapter 14: Seeking Out Subspaces of a Vector Space
• Investigating Properties Associated with Subspaces
• Finding a Spanning Set for a Vector Space
• Defining and Using the Column Space
• Connecting Null Space and Column Space
• Chapter 15: Scoring Big with Vector Space Bases
• Going Geometric with Vector Spaces
• Creating Bases from Spanning Sets
• Making the Right Moves with Orthogonal Bases
• Writing the Same Vector after Changing Bases
• Chapter 16: Eyeing Eigenvalues and Eigenvectors
• Defining Eigenvalues and Eigenvectors
• Solving for Eigenvalues and Eigenvectors
• Circling Around Special Circumstances
• Getting It Straight with Diagonalization
• Part V: The Part of Tens
• Chapter 17: Ten Real-World Applications Using Matrices
• Controlling Traffic
• Catching Up with Predator-Prey
• Creating a Secret Message
• Saving the Spotted Owl
• Migrating Populations
• Plotting Genetic Code
• Distributing the Heat
• Making Economical Plans
• Playing Games with Matrices
• Eating Right
• Chapter 18: Ten (Or So) Linear Algebra Processes You Can Do on Your Calculator
• Letting the Graph of Lines Solve a System of Equations
• Making the Most of Matrices
• Performing Row Operations
• Raising to Powers and Finding Inverses
• Determining the Results of a Markov Chain
• Solving Systems Using A–1*B
• Adjusting for a Particular Place Value
• Chapter 19: Ten Mathematical Meanings of Greek Letters
• Insisting That π Are Round
• Determining the Difference with Δ
• Summing It Up with Σ
• Row, Row, Row Your Boat with ρ
• Taking on Angles with θ
• Looking for a Little Variation with ε
• Taking a Moment with μ
• Looking for Mary’s Little λ
• Wearing Your ΦΒΚ Key
• Coming to the End with ω
• Glossary
• Index