Linear Algebra: An Interactive Introduction

Preliminaries
A Brief Introduction to ℝn: 0.00%
Introduction to Vectors: 0.00%
Length of a Vector: 0.00%
Vector Arithmetic: 0.00%
Standard Unit Vectors in ℝn: 0.00%
Unit Vector in the Direction of a Given Vector: 0.00%
Dot Product and its Properties: 0.00%
Dot Product and Angle: 0.00%
Orthogonal Projections: 0.00%
Cross Product and its Properties: 0.00%
Parametric Equations of Lines: 0.00%
Planes in ℝ3: 0.00%
Systems of Linear Equations
Introduction to Systems of Linear Equations: 0.00%
Augmented Matrix Notation and Elementary Row Operations: 0.00%
Gaussian Elimination and Rank: 0.00%
Iterative Methods for Solving Linear Systems: 0.00%
Big Ideas about Vectors
Linear Combinations of Vectors: 0.00%
Span: 0.00%
What Makes a Good Coordinate System?: 0.00%
Linear Independence: 0.00%
Matrices
Addition and Scalar Multiplication of Matrices: 0.00%
Matrix Multiplication: 0.00%
Block Matrix Multiplication: 0.00%
Transpose of a Matrix: 0.00%
Linear Systems as Matrix and Linear Combination Equations: 0.00%
Homogeneous Linear Systems: 0.00%
The Inverse of a Matrix: 0.00%
Elementary Matrices: 0.00%
LU Factorization: 0.00%
Subspaces of Rn
ℝn and Subspaces of ℝn: 0.00%
Introduction to Bases: 0.00%
Bases and Dimension: 0.00%
Subspaces of ℝn Associated with Matrices: 0.00%
Linear Transformations
Matrix Transformations: 0.00%
Geometric Transformations of the Plane: 0.00%
Introduction to Linear Transformations: 0.00%
Standard Matrix of a Linear Transformation from ℝn to ℝm: 0.00%
Composition and Inverses of Linear Transformations: 0.00%
Image and Kernel of a Linear Transformation: 0.00%
The Determinant
Finding the Determinant: 0.00%
Determinants, Areas, and Volumes: 0.00%
Elementary Row Operations and the Determinant: 0.00%
Properties of the Determinant: 0.00%
Tedious Proofs Concerning Determinants: 0.00%
Determinants and Inverses of Nonsingular Matrices: 0.00%
Eigenvalues
Describing Eigenvalues and Eigenvectors: 0.00%
The Characteristic Equation: 0.00%
Similar Matrices and Their Properties: 0.00%
Diagonalizable Matrices and Multiplicity: 0.00%
Gershgorin’s Theorem: 0.00%
The Power Method and the Dominant Eigenvalue: 0.00%
Orthogonality
Orthogonality and Projections: 0.00%
Least-Squares Approximation: 0.00%
Gram-Schmidt Orthogonalization: 0.00%
Orthogonal Complements and Decompositions: 0.00%
Orthogonal Matrices and Symmetric Matrices: 0.00%
Positive Definite Matrices: 0.00%
QR Factorization: 0.00%
SVD Decomposition: 0.00%
Abstract Vector Spaces
Abstract Vector Spaces: 0.00%
Bases and Dimension of Abstract Vector Spaces: 0.00%
Linear Transformations of Abstract Vector Spaces: 0.00%
Existence of the Inverse of a Linear Transformation: 0.00%
Isomorphic Vector Spaces: 0.00%
Matrices of Linear Transformations with Respect to Arbitrary Bases: 0.00%
Applications
Applications: 0.00%
Application to Network Flow: 0.00%
Application to Electrical Networks: 0.00%
Application to Chemical Equations: 0.00%
Application to Input-Output Economic Models: 0.00%
Application to Markov Chains: 0.00%
Curve Fitting: 0.00%
Application to Computer Graphics: 0.00%
Octave Exercises
Using Octave: 0.00%
Octave for Chapter 1: 0.00%
Octave for Chapter 2: 0.00%
Octave for Chapter 3: 0.00%
Octave for Chapter 4: 0.00%
Octave for Chapters 5-6: 0.00%
Octave for Chapter 7: 0.00%
Octave for Chapter 8: 0.00%
Octave for Chapter 9: 0.00%
Appendix
Triangle Inequality: 0.00%
Complex Numbers: 0.00%
Complex Matrices: 0.00%
Inner Product Spaces: 0.00%
Overall: 0%

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