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Computational Linear Algebra:
Notes and Questions for MATH 3325
Nicholas Long
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Front Matter
1
Solving Linear Systems
1.1
Warmup Problems
1.1.1
Application Warmup Problem
1.2
Solving Linear Systems
1.2.1
Elementary Operations
1.3
Consistency and Uniqueness Theorems
1.3.1
Writing Solution Sets
1.3.2
Determining Consistency/Uniqueness of Solutions
1.4
Geometric Interpretations and Applications
1.4.1
Geometric Interpretation of a Solution Set
1.4.2
Applications and Linear Algebra
1.5
Vectors and Vector Calculations
1.5.1
The Dot Product
1.6
Vector Equations
1.7
Span (both a noun and a verb)
1.7.1
Span as a Noun
1.7.2
Span as a Verb
1.8
Linear Independence
2
Matrices
2.1
Matrix Products and Equations
2.1.1
Matrix-Vector Products
2.1.2
The Matrix Equation
2.1.3
Linear Transformations
2.2
Matrix Operations
2.2.1
Addition and Transposition
2.2.2
Matrix Multiplication
2.2.3
Special Types of Matrices
2.3
Inverse Matrices
2.3.1
Computing Inverses
2.4
Invertible Matrix Theorem
2.5
Determinants
2.5.1
Computing Determinants
2.5.2
Properties of Determinants
2.6
A Motivating Example
2.7
Eigenvalues and Eigenvectors
3
Applications of Linear Algebra
3.1
Discrete Dynamical Systems
3.1.1
Predator-Prey Systems
3.1.2
Difference Equations and Linear Algebra
3.1.3
Types of Solutions to Two Dimensional Linear Difference Equations
3.2
Change of Coordinates
3.2.1
Same Eigenvalues, Different Eigenvectors
3.3
Continuous Dynamical Systems
3.3.1
Linear Systems of Ordinary Differential Equations
3.3.2
Converting Higher Order DEs to Systems
3.4
Graphics and Linear Algebra
3.5
Operators
3.5.1
Linear Operators
3.5.2
Boundary Value Problems
3.6
Vector Spaces: The Big Idea
3.7
Subspaces
3.8
Motivating Activity
3.9
Fourier Series
Backmatter
Colophon
Colophon
This book was authored in PreTeXt.
