- Subjects
- Published
-
San Francisco :
No Starch Press
2012.
- Language
- English
Japanese - Corporate Author
- Main Author
- Corporate Author
- Other Authors
- 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.