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The Manga Guide to Linear Algebra

Book Description

Follow along in The Manga Guide to Linear Algebra as Reiji takes Misa from the absolute basics of this tricky subject through mind-bending operations like performing linear transformations, calculating determinants, and finding eigenvectors and eigenvalues. With memorable examples like miniature golf games and karate tournaments, Reiji transforms abstract concepts into something concrete, understandable, and even fun.

Table of Contents

  1. Preface
  2. Prologue: Let the Training Begin! (1/2)
  3. Prologue: Let the Training Begin! (2/2)
  4. 1: What Is Linear Algebra?
    1. An Overview of Linear Algebra (1/2)
    2. An Overview of Linear Algebra (2/2)
  5. 2: The Fundamentals
    1. Number Systems
    2. Implication and Equivalence
      1. Propositions
      2. Implication
      3. Equivalence
    3. Set Theory
      1. Sets
      2. Set Symbols
      3. Subsets
    4. Functions
      1. Images
      2. Domain and Range
      3. Onto and One-to-One Functions
      4. Inverse Functions
      5. Linear Transformations
    5. Combinations and Permutations (1/2)
    6. Combinations and Permutations (2/2)
    7. Not All “Rules for Ordering” Are Functions
  6. 3: Intro to Matrices
    1. What Is a Matrix?
    2. Matrix Calculations
      1. Addition
      2. Subtraction
      3. Scalar Multiplication
      4. Matrix Multiplication
    3. Special Matrices
      1. Zero Matrices
      2. Transpose Matrices
      3. Symmetric Matrices
      4. Upper Triangular and Lower Triangular Matrices
      5. Diagonal Matrices
      6. Identity Matrices
  7. 4: More Matrices
    1. Inverse Matrices
    2. Calculating Inverse Matrices (1/2)
    3. Calculating Inverse Matrices (2/2)
    4. Determinants
    5. Calculating Determinants (1/3)
    6. Calculating Determinants (2/3)
    7. Calculating Determinants (3/3)
    8. Calculating Inverse Matrices Using Cofactors
      1. Mij
      2. Cij
      3. Calculating Inverse Matrices
    9. Using Determinants
    10. Solving Linear Systems with Cramer's Rule
  8. 5: Introduction to Vectors
    1. What Are Vectors? (1/2)
    2. What Are Vectors? (2/2)
    3. Vector Calculations
    4. Geometric Interpretations
  9. 6: More Vectors
    1. Linear Independence (1/2)
    2. Linear Independence (2/2)
    3. Bases (1/2)
    4. Bases (2/2)
    5. Dimension
      1. Subspaces (1/2)
      2. Subspaces (2/2)
      3. Basis and Dimension
    6. Coordinates
  10. 7: Linear Transformations
    1. What Is a Linear Transformation? (1/2)
    2. What Is a Linear Transformation? (2/2)
    3. Why We Study Linear Transformations
    4. Special Transformations
      1. Scaling
      2. Rotation
      3. Translation
      4. 3-D Projection
    5. Some Preliminary Tips
    6. Kernel, Image, and the Dimension Theorem for Linear Transformations
    7. Rank
      1. Calculating the Rank of a Matrix (1/2)
      2. Calculating the Rank of a Matrix (2/2)
    8. The Relationship Between Linear Transformations and Matrices
  11. 8: Eigenvalues and Eigenvectors (1/2)
  12. 8: Eigenvalues and Eigenvectors (2/2)
    1. What Are Eigenvalues and Eigenvectors?
    2. Calculating Eigenvalues and Eigenvectors
    3. Calculating the pth Power of an nxn Matrix
    4. Multiplicity and Diagonalization
      1. A Diagonalizable Matrix with an Eigenvalue Having Multiplicity 2
      2. A Non-Diagonalizable Matrix with a Real Eigenvalue Having Multiplicity 2
  13. Epilogue (1/3)
  14. Epilogue (2/3)
  15. Epilogue (3/3)
  16. Online Resources
    1. The Appendixes
    2. Updates
  17. Index (1/2)
  18. Index (2/2)