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Discover Linear Algebra
Jeremy Sylvestre
Contents
Index
Prev
Up
Next
Contents
Prev
Up
Next
Front Matter
Colophon
Author Biography
Preface
I
Systems of Equations and Matrices
1
Systems of linear equations
Discovery guide
Terminology and notation
Concepts
Examples
2
Solving systems using matrices
Discovery guide
Terminology and notation
Concepts
Examples
Theory
3
Using systems of equations
Discovery guide
Examples
Terminology and notation
Theory
4
Matrices and matrix operations
Discovery guide
Terminology and notation
Concepts
Examples
Theory
5
Matrix inverses
Discovery guide
Terminology and notation
Concepts
Examples
Theory
6
Elementary matrices
Discovery guide
Terminology and notation
Concepts
Examples
Theory
7
Special forms of square matrices
Discovery guide
Terminology and notation
Concepts
Examples
Theory
8
Determinants
Discovery guide
Terminology and notation
Concepts
Examples
Theory
9
Determinants versus row operations
Discovery guide
Concepts
Examples
Theory
10
Determinants, the adjoint, and inverses
Discovery guide
Terminology and notation
Concepts
Examples
Theory
11
Complex systems and matrices
Motivation
Terminology and notation
Examples
Theory
II
Vector Spaces
12
Introduction to vectors
Discovery guide
Terminology and notation
Concepts
Examples
Theory
13
Geometry of vectors
Discovery guide
Terminology and notation
Concepts
Examples
Theory
14
Orthogonal vectors
Discovery guide
Terminology and notation
Concepts
Examples
Theory
15
Geometry of linear systems
Discovery guide
Terminology and notation
Concepts
Examples
16
Abstract vector spaces
Discovery guide
Motivation
Terminology and notation
Concepts
Examples
Theory
17
Subspaces
Discovery guide
Terminology and notation
Concepts
Examples
Theory
More examples
18
Linear independence
Discovery guide
Terminology and notation
Concepts
Examples
Theory
19
Basis and Coordinates
Discovery guide
Terminology and notation
Concepts
Examples
Theory
20
Dimension
Discovery guide
Terminology and notation
Concepts
Examples
Theory
21
Column, row, and null spaces
Discovery guide
Terminology and notation
Concepts
Examples
Theory
22
Change of basis
Discovery guide
Terminology and notation
Concepts
Examples
Theory
23
Complex vector spaces
Motivation
Terminology and notation
Concepts
Examples
III
Introduction to Matrix Forms
24
Eigenvalues and eigenvectors
Discovery guide
Terminology and notation
Motivation
Concepts
Examples
Theory
25
Diagonalization
Discovery guide
Terminology and notation
Motivation
Concepts
Examples
Theory
26
Similarity
Discovery guide
Terminology and notation
Concepts
Examples
Theory
27
Application to systems of differential equations
Discovery guide
Terminology and notation
Concepts
Examples
28
Block-diagonal form
Motivation
Discovery guide
Terminology and notation
Concepts
Examples
Theory
29
Scalar-triangular form
Motivation
Discovery guide
Terminology and notation
Concepts
Examples
Theory
30
Triangular block form
Motivation
Examples
Terminology and notation
Concepts
Theory
31
Consequences of triangular block form
Discovery guide
Terminology and notation
Concepts
Examples
Theory
32
Elementary nilpotent form
Discovery guide
Motivation
Terminology and notation
Concepts
Examples
Theory
33
Triangular-block nilpotent form
Motivation
Terminology and notation
Discovery guide
Concepts
Examples
Theory
34
Jordan normal form
Motivation
Terminology and notation
Concepts
Examples
Theory
35
Summary of matrix forms
Diagonal form
Block-diagonal form
Scalar-triangular form
Triangular-block form
Elementary nilpotent form
Triangular-block nilpotent form
Jordan normal form
IV
Inner Product Spaces
36
Abstract inner product spaces
Motivation
Discovery guide
Terminology and notation
Concepts
Examples
Theory
37
Orthgonality
Discovery guide
Terminology and notation
Concepts
Examples
Theory
38
Orthogonal projection and best approximation
Concepts
Terminology and notation
Examples
Theory
39
Matrix adjoints
Discovery guide
Terminology and notation
Concepts
Examples
Theory
40
Orthogonal/unitary diagonalization
Motivation
Discovery guide
Terminology and notation
Concepts
Examples
Theory
41
Quadratic forms
Discovery guide
Terminology and notation
Concepts
Examples
Theory
V
Linear Transformations
42
Matrix and linear transformations
Discovery guide
Terminology and notation
Concepts
Examples
Theory
43
Kernel and image
Discovery guide
Terminology and notation
Concepts
Examples
Theory
44
Compositions and isomorphisms
Discovery guide
Terminology and notation
Concepts
Examples
Theory
45
The matrix of a linear transformation
Discovery guide
Terminology and notation
Concepts
Examples
Theory
46
Similarity of linear operators
Terminology and notation
Concepts
Examples
Theory
Back Matter
A
Complex numbers
Motivation
The field of complex numbers
The complex plane
B
Sage Tutorials
Basics
Linear algebra basics
Diagonal form
Scalar-triangular form
Triangular block form
Gram-Schmidt orthogonalization
Best approximation
Orthogonal/unitary diagonalization
C
GNU Free Documentation License
Bibliography
Index
Colophon
Authored in PreTeXt
Colophon
Colophon
This book was authored in MathBook XML.