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Linear Algebra:
Notes for MATH 341
Mitchel T. Keller, Nicholas Long
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Front Matter
Colophon
Preface
0
Getting Started
0.1
Setting the Stage
0.2
What is a sandwich?
0.3
Warmup Problems
Warmup Problems
1
Getting Started
1.1
Introduction to mathematical arguments
1.2
Writing First Proofs
Practicing Writing Proofs
2
Solving Systems
2.1
Solving Linear Systems
Elementary Operations
2.2
Vector and Matrix Equations
2.3
Solution Sets of Linear Systems
2.4
Matrix Operations
Addition and Transposition
Special Types of Matrices
Matrix Multiplication
3
Vector Spaces
3.1
Definitions
3.2
Subspaces
3.3
Span
3.4
Linear Independence
3.5
Linear Transformations
A Digression Into Functions
Functions on vector spaces
4
Connecting Ideas
4.1
Basis and Dimension
4.2
Invertible Matrices
Elementary Matrices
Computing Inverses
Invertible Matrix Theorem
4.3
Determinants
Computing Determinants
Properties of Determinants
4.4
Eigenvalues and Eigenvectors
5
Inner Product Spaces
5.1
Inner Products
5.2
Orthogonal Complements
5.3
Orthonormal Bases
Section
0.2
What is a sandwich?
We then do Matt Salomone’s “Is it a sandwich?” activity.
