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Linear Algebra with SageMath:
Learn math with open-source software
Allaoua Boughrira, Hellen Colman, Samuel Lubliner
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\(\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)
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
2.1
Vectors
2.2
Matrices
3
System of Equations
3.1
Solving Equations
4
System of Equations with Matrices
4.1
Row Reduction
4.2
Systems of Equations with Matrices
5
Vectors
5.1
Operations with Vectors
5.1.1
Vector Arithmetic
5.2
Operations on Vectors
5.2.1
Normalized Vector
5.2.2
Cross and Dot Products of Vectors
5.2.3
Conjugate of a Complex Vector
6
Matrices
6.1
Special Matrices
6.2
Operations With Matrices
6.2.1
Matrix Arithmetic
6.3
Operations On Matrices
6.3.1
Determinant and Inverse of a Matrix
6.3.2
Transpose and Conjugate of a Matrix
6.3.3
LU Decomposition of a Matrix
7
Equations of Lines and Planes
8
Orthogonality
9
Linear Transformation From R Pow N to R Pow M
10
Eigenvectors and Eigenvalues
11
Diagonalization
12
General Vector Spaces
13
Linear Independence
14
General Linear Transformations
Back Matter
References
Colophon
Index
Preface
From the Student Authors
PLACEHOLDER
Allaoua Boughrira and Samuel Lubliner
