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Matrix Algebra from a Geometric Point of View
Christopher Eagle
Contents
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Contents
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Front Matter
Acknowledgements
Colophon
1
Systems of Linear Equations
Systems of linear equations
Gauss-Jordan elimination
2
Vectors in
\(\mathbb{R}^n\)
Vectors and basic operations
Geometry: The dot product
Lines and planes in
\(\mathbb{R}^2\)
and
\(\mathbb{R}^3\)
3
Linear Independence, Span, Subspaces
Span
Linear independence
Systems of linear equations revisited
Subspaces of
\(\mathbb{R}^n\)
4
Linear Transformations and Matrix Algebra
Linear transformations
Operations on matrices
Matrix multiplication
Matrix inverses
Determinants
Subspaces associated to matrices
5
Eigenvalues, Eigenvectors, and Diagonalization
Eigenvalues and eigenvectors
Diagonalization
6
Vector Geometry Revisited
Orthogonality
Orthogonal projections
Orthogonal matrices
The Spectral Theorem
Back Matter
References
Authored in PreTeXt
Colophon
Colophon
©2020-2022 Christopher Eagle
Creative Commons BY-SA-NC