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An Introduction to Matrix Computations in Python:
Just the basics
Nicole Seaders and Claire Burke
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Front Matter
0
Prologue
1
Basics, Modules, and Graphing
1.1
Variables
Naming Variables
Arithmetic and Comments in Python
More about Variables
Syntax and Semantic errors
Exercises
1.2
Python Packages and NumPy
Importing the package NumPy
Standard functions in NumPy
NumPy arrays
Exercises
1.3
Matplotlib and 2D graphing
Creating a graph or plot
Curves in 2D
Scatter Plots in 2D
Parametric Curves in 2D
Titles and Axes Labels
Customizing
Vectors in 2D
Multiple plots in the same figure
Exercises
1.4
Matplotlib and 3D graphing
3D axes
Parametric Curves in 3D
Surfaces and scatterplots in 3D
Axes and Labels
Plotting Multiple Surfaces
Customizing
Exercises
1.5
Basic Animation
Creating a .gif in Matplotlib
Creating an interactive slider
Student Showcase
Exercises
2
Matrix Algebra in Python
2.1
Solving and Graphing Systems of Linear Equations
Row Reduction
Graphing solutions to systems of equations
Graphing vector equations and their solutions
Converting between Numpy arrays and Sympy Matrices
Round-off error in Sympy’s rref()
Exercises
2.2
Matrix Arithmetic
NumPy vs SymPy
Basic Matrices
Matrix Arithmetic
Matrix Multiplication
Matrix Inverses
Solving Matrix Equations via Inverses
Ill-Conditioned Matrices
Exercises
2.3
Matrix Transformations
Computing Matrix Transformations
Visualizing a Matrix Transformation
Animating Matrix Transformations
Exercises
2.4
Determinants
What is the determinant?
Computing the Determinant
Determinants and Systems of Linear Equations
Numerically Solving System of Equations
Ill-conditioned Matrices
Exercises
2.5
Eigenthings
Computing Eigenthings
Visualizing with Eigenthings
Diagonalization
Complex Eigen-thing Decomposition
Exercises
3
Appendix
3.1
Samples of various pretext formats
What happens if I do this?
Reading Questions
Backmatter
Colophon
Colophon
This book was authored in PreTeXt.
