Reiji wants two things in life: a black belt in karate and Misa, the girl of his dreams. Luckily, Misa's big brother is the captain of the university karate club and is ready to strike a deal: Reiji can join the club if he tutors Misa in linear algebra.
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.
As you follow Misa through her linear algebra crash course, you'll learn about:
• Basic vector and matrix operations such as addition, subtraction, and multiplication
• Linear dependence, independence, and bases
• Using Gaussian elimination to calculate inverse matrices
• Subspaces, dimension, and linear span
• Practical applications of linear algebra in fields like computer graphics, cryptography, and engineering
But Misa's brother may get more than he bargained for as sparks start to fly between student and tutor. Will Reiji end up with the girl—or just a pummeling from her oversized brother? Real math, real romance, and real action come together like never before in The Manga Guide to Linear Algebra.
Author(s): Shin Takahashi, Iroha Inoue
Series: Manga guide
Edition: 1
Publisher: No Starch Press
Year: 2012
Language: English
Commentary: Publisher's PDF
Pages: 264
City: San Francisco, CA
Tags: Popular Science; Linear Algebra; Mathematics; Children
Preface......Page 13
Prologue: Let the Training Begin!
......Page 15
1: What Is Linear Algebra?
......Page 23
An Overview of Linear Algebra......Page 28
2: The Fundamentals
......Page 35
Number Systems......Page 39
Propositions......Page 41
Implication......Page 42
Equivalence......Page 43
Sets......Page 44
Set Symbols......Page 46
Subsets......Page 47
Functions......Page 49
Images......Page 54
Domain and Range......Page 58
Onto and One-to-One Functions......Page 60
Inverse Functions......Page 62
Linear Transformations......Page 64
Combinations and Permutations......Page 69
Not All “Rules for Ordering” Are Functions......Page 75
3: Intro to Matrices
......Page 77
What Is a Matrix?......Page 80
Addition......Page 84
Subtraction......Page 85
Scalar Multiplication......Page 86
Matrix Multiplication......Page 87
Zero Matrices......Page 91
Transpose Matrices......Page 92
Upper Triangular and Lower Triangular Matrices......Page 93
Diagonal Matrices......Page 94
Identity Matrices......Page 96
4: More Matrices
......Page 99
Inverse Matrices......Page 100
Calculating Inverse Matrices......Page 102
Determinants......Page 109
Calculating Determinants......Page 110
Mij......Page 122
Cij......Page 123
Calculating Inverse Matrices......Page 124
Solving Linear Systems with Cramer's Rule......Page 125
5: Introduction to Vectors
......Page 127
What Are Vectors?......Page 130
Vector Calculations......Page 139
Geometric Interpretations......Page 141
6: More Vectors
......Page 145
Linear Independence......Page 146
Bases......Page 154
Dimension......Page 163
Subspaces......Page 164
Basis and Dimension......Page 170
Coordinates......Page 175
7: Linear Transformations
......Page 177
What Is a Linear Transformation?
......Page 180
Why We Study Linear Transformations......Page 187
Special Transformations......Page 192
Scaling......Page 193
Rotation......Page 194
Translation......Page 196
3-D Projection......Page 199
Some Preliminary Tips......Page 202
Kernel, Image, and the Dimension Theorem for Linear Transformations......Page 203
Rank......Page 207
Calculating the Rank of a Matrix......Page 210
The Relationship Between Linear Transformations and Matrices......Page 217
8: Eigenvalues and Eigenvectors
......Page 219
What Are Eigenvalues and Eigenvectors?......Page 225
Calculating Eigenvalues and Eigenvectors......Page 230
Calculating the pth Power of an nxn Matrix......Page 233
Multiplicity and Diagonalization......Page 238
A Diagonalizable Matrix with an Eigenvalue Having Multiplicity 2......Page 239
A Non-Diagonalizable Matrix with a Real Eigenvalue Having Multiplicity 2......Page 241
Epilogue......Page 245
Updates......Page 257
Index......Page 259
