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TBIL Activities for Understanding Linear Algebra
Jennifer Nordstrom
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Front Matter
Colophon
Acknowledgements
Preface
1
TBIL Activities: Systems of Equations
1.1
What can we expect
1.2
Finding solutions to systems of linear equations
1.3
Computation with Sage
1.4
Pivots and their influence on solution spaces
2
TBIL Activities: Vectors, Matrices, and Linear Combinations
2.1
Vectors and linear combinations
2.2
Matrix multiplication and linear combinations
2.3
The span of a set of vectors
2.4
Linear independence
2.5
Matrix transformations
2.5.1
Applications of matrix transformations
2.6
The geometry of matrix transformations
3
TBIL Activities: Invertibility, Bases, and Coordinate Systems
3.1
Invertibility
3.2
Bases and coordinate systems
3.3
Image Compression
3.4
Determinants
3.5
Subspaces of
R
p
4
TBIL Activities: Eigenvalues and Eigenvectors
4.1
An introduction to eigenvalues and eigenvectors
4.2
Finding eigenvalues and eigenvectors
4.3
Diagonalization, similarity, and powers of a matrix
4.4
Dynamical Systems
4.5
Markov chains and Google's PageRank algorithm
5
TBIL Activities: Orthogonality
5.1
The dot product
5.2
Orthogonal complements and the matrix transpose
Backmatter
Index
Colophon
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TBIL Activities for Understanding Linear Algebra
Jennifer Nordstrom
Mathematics
Linfield University
April 1, 2023
Colophon
Acknowledgements
Preface
