Section 1.3 Textbook
The textbook (primary resource) for this course is the distributed notes Let’s Get Linear!, which will be edited dynamically through the term and available online. This departmental web resource is your secondary source, and the third source will be A First Course in Linear Algebra by Ken Kuttler. A pdf file is located at here. Make use of all three as you see fit. Where they differ in approach or notation our course will exclusively require you to use the conventions found in our text Let’s Get Linear!.
The course will be covered by the following sections of Kuttler's textbook:
CONTENTS
1 Systems of Equations
1.1 Systems of Equations, Geometry
1.2 Systems Of Equations,Algebraic Procedures
1.2.1 Elementary Operations
1.2.2 Gaussian Elimination
1.2.3 Uniqueness of the Reduced Row-Echelon Form
1.2.4 Rank and Homogeneous Systems
2 Matrices
2.1 Matrix Arithmetic
2.1.1 Addition of Matrices
2.1.2 Scalar Multiplication of Matrices
2.1.3 Multiplication of Matrices
2.1.4 The ijth Entry of a Product
2.1.5 Properties of Matrix Multiplication
2.1.6 The Transpose
2.1.7 The Identity and Inverses
2.1.8 Finding the Inverse of a Matrix
2.1.9 Elementary Matrices
2.1.10 More on Matrix Inverses
3 Determinants
3.1 Basic Techniques and Properties
3.1.1 Cofactors and 2×2 Determinants
3.1.2 The Determinant of a Triangular Matrix
3.1.3 Properties of Determinants
3.1.4 Finding Determinants using Row Operations
3.2 Applications of the Determinant
3.2.1 A Formula for the Inverse
3.2.2 Cramer’s Rule
3.2.3 Polynomial Interpolation
4 R^n
4.1 Vectors in R^n
4.2 Algebra in R^n
4.2.1 Addition of Vectors in R^n
4.2.2 Scalar Multiplication of Vectors in R^n
4.3 Geometric Meaning of Vector Addition
4.4 Length of a Vector
4.5 Geometric Meaning of Scalar Multiplication
4.6 Parametric Lines
4.7 The Dot Product
4.7.1 The Dot Product
4.7.2 The Geometric Significance of the Dot Product
4.7.3 Projections
4.8 Planes in R^n
4.9 The Cross Product
4.9.1 The Box Product
4.10 Spanning, Linear Independence and Basis in R^n
4.10.1 Spanning Set of Vectors
4.10.2 Linearly Independent Set of Vectors
4.10.4 Subspaces and Basis
4.10.5 Row Space, Column Space, and Null Space of a Matrix
4.11 Orthogonality and the Gram Schmidt Process
4.11.1 Orthogonal and Orthonormal Sets
4.11.2 Orthogonal Matrices
4.11.3 Gram-Schmidt Process
4.11.4 Orthogonal Projections
4.11.5 Least Squares Approximation
5 Linear Transformations
5.1 Linear Transformations
5.2 The Matrix of a LinearTransformation
5.3 Properties of Linear Transformations
5.4 Special Linear Transformations in R^2
5.5 Linear Transformations which are One To One or Onto
5.6 The General Solution of a Linear System
6 Complex Numbers
6.1 Complex Numbers
6.2 Polar Form
6.3 Roots of Complex Numbers
6.4 The Quadratic Formula
7 Spectral Theory
7.1 Eigenvalues and Eigenvectors of a Matrix
7.1.1 Definition of Eigenvectors and Eigenvalues
7.1.2 Finding Eigenvectors and Eigenvalues
7.1.3 Eigenvalues and Eigenvectors for Special Types of Matrices
7.2 Diagonalization
7.2.1 Diagonalizing a Matrix
7.2.2 Complex Eigenvalues
7.3 Applications of Spectral Theory
7.3.1 Raising a Matrix to a High Power
7.3.2 Raising a Symmetric Matrix to a High Power
7.3.3 Markov Matrices
7.4 Orthogonality
7.4.1 Orthogonal Diagonalization
7.4.2 Positive Definite Matrices
7.4.3 QR Factorization
7.4.4 Quadratic Forms