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Manitoba linear algebra
Michael Doob
Contents
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Contents
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Title Page
1
Systems of Linear Equations
2
Matrix Theory
3
The Determinant
4
Vectors in Euclidean
n
space
5
Eigenvalues and eigenvectors
6
Linear transformations
7
Additional Topics
Authored in PreTeXt
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Chapter
4
Vectors in Euclidean
n
space
4.1
Initial definitions
4.2
The dot product of vectors in
R
n
4.3
Lines, planes, and generalizations
4.4
Equations of lines in
R
3
4.5
Cross Product of Vectors in
R
3
4.6
Equations of Planes in
R
3
4.7
Projections in
R
2
and
R
n
4.8
Geometric applications
4.9
Linear independence, spanning and bases in
R
n
4.10
Bases and coordinates