Linear Algebra Textbook
Linear Algebra Textbook
Table of Contents
Chapter 1
Introduction to Matrices and Linear Systems
Chapter 2
Deep Dive into Linear Algebra
Chapter 3
Beyond Linear Algebra
1
Introduction to Matrices and Linear Systems
1.1
Linear Geometry: Vectors in Space and Angle & Length
Vectors in Space
Vector Length
Angle between Vectors
Problem Set
1.2
Dot Product
Problem Set
1.3
Solving Linear Equations
Gauss’s Method
Problem Set
1.4
Row Echelon Form & Reduced Row Echelon Form
1.4.1
Reduced Row Echelon Form
Equivalence Relations
Linear Combination Lemma
Supporting Theorems
1.5
Determinants and Inverse Matrices
1.5.1
Determinants
1.5.2
Cofactor Expansion
1.5.3
Inverses of Matrices
1.6
Labs
Geology Lab
1.7
Coding Labs
Linear Geometry and Matrices Lab (
1.1-1.2
:
Linear Geometry
and
Matrix Definitions and Operations
)
Linear Systems Lab (
1.3 & 1.4
:
Solving Linear Systems
and
REF & RREF
)
Determinants, Cofactor Expansion, and Inverse Matrices Lab (1.5:
Determinants & Invertibility
)
1.8
Projects
Truss Project (
1.1-1.3
:
Vector Spaces Applications
)
Encryption Project (
1.4-1.5
:
Matrix Applications
)
2
Deep Dive into Linear Algebra
2.1
Definition of Vector Space
Extend to
\(\mathbb{R^{n}}\)
Subspaces
Complex Numbers
Subspaces & Spanning Sets
Solutions to Assorted Problems:
Problem Set
2.2
Linear Independence, Basis, Dimension
Linear Independence
Basis
Dimension
Fundamental Subspaces
Solutions to Assorted Problems:
2.3
Orthogonal Matrices, Change of Basis
Orthogonal Vector
Orthogonal Vector
Orthogonal Matrix
Orthonormal Basis
2.4
Projection and Change of Basis
Projection:
Projection into Subspaces:
Example:
The Gram-Schmidt Process:
Example:
2.5
Labs
Fields Lab (2.1:
Vector Spaces
)
Chemical Balancing Lab (2.2:
Linear Independence, Basis, and Dimension
)
2.6
Coding Labs
Dimensional Analysis (2.2:
Linear Independence, Basis, and Dimension
)
2.6.1
Orthogonality, Gram-Schmidt Process, and SVD (2.4-2.5:
Projects & Fundamental Theorem of Linear Algebra
)
2.6.2
Coding Key
3
Beyond Linear Algebra
4
References
4.1
Linear Algebra Resource Board
4.2
R Programming Resources
Published with bookdown
Linear Algebra
Linear Algebra
2023-05-02
Linear Algebra Textbook
