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Linear Algebra with SageMath:
Learn math with open-source software
Allaoua Boughrira, Hellen Colman, Michael Kattner, Samuel Lubliner
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Front Matter
Preface
Acknowledgements
From the Student Authors
Authors and Contributors
Colophon
1
Getting Started
1.1
Intro to Sage
1.1.1
Sage as a Calculator
1.1.2
Variables and Names
1.2
Data Types
1.3
Flow Control Structures
1.3.1
Conditional Statements
1.3.2
Iteration
1.3.2.1
List Comprehension
1.3.3
Other Flow Control Structures
1.4
Defining Functions
1.5
Object-Oriented Programming
1.5.1
Objects in Sage
1.5.2
Dot Notation and Methods
1.5.3
Sage’s Set Class
1.6
Display Values
1.7
Debugging
1.8
Documentation
1.9
Miscellaneous Features
1.9.1
Reading and Writing Files in Sage
1.9.2
Executing Shell Commands in Sage
1.9.3
Importing and Exporting Data (CSV, JSON, TXT)
1.9.4
Using External Libraries in Sage
1.10
Run Sage in the browser
2
Vectors and Matrices, The Basics
2.1
Vectors
2.2
Matrices
3
System of Equations
3.1
Solving Equations
3.2
Solving Systems of Equations
4
System of Equations with Matrices
4.1
Gauss-Jordan Elimination
4.1.1
Augmented Matrix
4.1.2
RREF
4.2
Systems of Equations with Matrices
4.2.1
Differences in Solutions
5
Vectors
5.1
Operations with Vectors
5.2
Dot and Cross Products
6
Matrices
6.1
Special Matrices
6.2
Operations With Matrices
6.3
Transpose, Conjugate and Adjoint Matrix
7
Determinants
7.1
Determinant and Inverse
7.1.1
Determinant of Matrix
7.1.2
Inverse of Matrix
7.1.3
Minors, Cofactors and the Adjugate Matrix
8
LU Decomposition
8.1
LU Decomposition
9
Equations of Lines and Planes
10
Orthogonality
10.1
Normalized Vector
11
Linear Transformation From R Pow N to R Pow M
12
Eigenvectors and Eigenvalues
12.1
Eigenvectors
12.1.1
Eigenvectors of Matrices
13
Diagonalization
14
General Vector Spaces
15
Linear Independence
16
General Linear Transformations
Back Matter
References
Colophon
Index
Chapter
4
System of Equations with Matrices
Systems of linear equations can be interpreted as matrices in order to make solving them more efficient as the number of variables grows. This chapter shows how to use Sage to construct and solve these matrices.
4.1
Gauss-Jordan Elimination
4.2
Systems of Equations with Matrices
