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
1.2
Dot Product
1.3
Solving Linear Equations
Gauss’s Method
1.4
Row Echelon Form
1.5
Reduced Row Echelon Form
1.6
Equivalence Relations
1.7
Linear Combination Lemma
Supporting Theorems
2
Deep Dive into Linear Algebra
2.1
Definition of Vector Space
Extend to
\(\mathbb{R^{n}}\)
2.1.1
Subspaces
2.1.2
Complex Numbers
2.1.3
Subspaces & Spanning Sets
2.1.4
Solutions to Assorted Problems:
2.2
Linear Independence, Basis, Dimension
2.2.1
Linear Independence
2.2.2
Basis
2.2.3
Dimension
2.2.4
Fundamental Subspaces
2.2.5
Solutions to Assorted Problems:
2.3
Orthogonal Matrices, Change of Basis
2.3.1
Orthogonal Vector
2.3.2
Orthogonal Vector
2.3.3
Orthogonal Matrix
2.3.4
Orthonormal Basis
2.4
Projection and Change of Basis
2.4.1
Projection:
2.4.2
Projection into Subspaces:
2.4.3
Example:
2.4.4
The Gram-Schmidt Process:
2.4.5
Example:
3
Beyond Linear Algebra
References
4
examples
5
3Blue1Brown videos
6
MIT CourseWave
Published with bookdown
Linear Algebra
3
Beyond Linear Algebra