The manga guide to linear algebra

Shin Takahashi

Book - 2012

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Subjects
Published
San Francisco : No Starch Press 2012.
Language
English
Japanese
Corporate Author
Trend-pro Co
Main Author
Shin Takahashi (-)
Corporate Author
Trend-pro Co (-)
Other Authors
Iroha Inoue (-)
Item Description
Includes index.
Physical Description
ix, 247 pages : illustrations ; 25 cm
ISBN
9781593274139
  • 1. What is linear algebra?
  • Overview of linear algebra
  • 2. The fundamentals
  • Number systems
  • Implication and equivalence
  • Propositions
  • Set theory
  • Sets
  • Set symbols
  • Subsets
  • Functions
  • Images
  • Domain and range
  • Onto and one-to-one functions
  • Inverse functions
  • Linear transformations
  • Combinations and permutations
  • Not all "rules for ordering" are functions
  • 3. Intro to matrices
  • What is a matrix?
  • Matrix calculations
  • Addition
  • Subtraction
  • Scalar multiplication
  • Matrix multiplication
  • Special matrices
  • Zero matrices
  • Transpose matrices
  • Symmetric matrices
  • Upper triangular and lower triangular matrices
  • Diagonal matrices
  • Identity matrices
  • 4. More matrices
  • Inverse matrices
  • Calculating inverse matrices
  • Determinants
  • Calculating determinants
  • Calculating inverse matrices using cofactors
  • Using determinants
  • Solving linear systems with Cramer's Rule
  • 5. Introduction to vectors
  • What are vectors?
  • Vector calculations
  • Geometric interpretations
  • 6. More vectors
  • Linear independence
  • Bases
  • Dimension
  • subspaces
  • Basis and dimension
  • Coordinates
  • 7. Linear transformations
  • what is a linear transformation?
  • Why we study linear transformations
  • Special transformations
  • Scaling
  • Rotation
  • Translation
  • 3-D projection
  • Kernel, image, and the dimension theorem for linear transformations
  • Rank
  • Calculating the rank of a matrix
  • The relationship between linear transformations and matrices
  • 8. Eigenvalues and eigenvectors
  • What are eigenvalues and eigenvectors?
  • Calculating eigenvalues and eigenvectors
  • Calculating the pth power of an nxn matrix
  • Multiplicity and diagonalization.
Review by Choice Review

This book is the second collaboration for analyst/author Takahashi, illustrator Inoue, and Trend-pro. Between them, they have authored several manga guides over the last four years (e.g., The Manga Guide to Statistics, CH, Apr'09, 46-4500). The book's organization is similar to other mathematics works, but it also includes a prologue, epilogue, and a list of relevant online resources. The text incorporates the learning of math with taking karate and a possible romance between a tutor and the karate instructor's sister. The story form may be beneficial when students want to read ahead. Takahashi explains the fundamentals of each concept and gives examples that can be applied in the real world. The first chapter provides a list of professional areas where linear algebra can be used and talks about which ones use the field to its fullest potential. Chapter 3 introduces matrices and different matrix operations. Even though this chapter is only 20 pages long, the discussions are clear, making the basics comprehensible to students. Chapter 7 explains the importance of studying linear transformations. This book would benefit readers who are taking linear algebra for the first time, or those who may need a refresher in the concepts of the subject. Summing Up: Recommended. Students of all levels and general readers. K. D. Holton Tallahasee Community College

Copyright American Library Association, used with permission.