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Introduction to algebra
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II · Linear algebra
Chapter II.4
Affine and Euclidean point spaces
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II.4.1 · Affine spaces
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II.4.2 · Euclidean
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II.4.3 · Groups and geometries
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II.4.4 · Spaces with an indefinite metric
Section II.4.1
Affine spaces
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Subsection II.4.1.1
Definition of an affine space
Subsection II.4.1.2
Isomorphism
Subsection II.4.1.3
Coordinates
Subsection II.4.1.4
Affine subspaces
Subsection II.4.1.5
Barycentric coordinates
Subsection II.4.1.6
Affine-linear functions and systems of linear equations
Subsection II.4.1.7
Relative position of planes
Section II.4.2
Euclidean
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Subsection II.4.2.1
Euclidean metric
Subsection II.4.2.2
Distance from a point to a plane
Subsection II.4.2.3
Distance between planes
Subsection II.4.2.4
The Gram determinant and the volume of a parallelepiped
Section II.4.3
Groups and geometries
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Subsection II.4.3.1
Affine group
Subsection II.4.3.2
Euclidean space motions
Subsection II.4.3.3
Group of isometries
Subsection II.4.3.4
Linear geometry corresponding to the group
Subsection II.4.3.5
Affine transformations of Euclidean space
Subsection II.4.3.6
Convex sets
Section II.4.4
Spaces with an indefinite metric
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Subsection II.4.4.1
Indefinite metric
Subsection II.4.4.2
Pseudo-Euclidean motions
Subsection II.4.4.3
The Lorentz group
Subsection II.4.4.4
The proper Lorentz group