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Introduction to algebra
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II · Linear algebra
Chapter II.5
Quadrics
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II.5.1 · Quadratic functions
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II.5.2 · Quadrics in affine and Euclidean spaces
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II.5.3 · Projective spaces
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II.5.4 · Quadrics in projective space
Section II.5.1
Quadratic functions
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Subsection II.5.1.1
Quadratic functions on affine space
Subsection II.5.1.2
Central points for a quadratic function
Subsection II.5.1.3
Reducing a quadratic function to canonical form
Subsection II.5.1.4
Quadratic functions on Euclidean space
Section II.5.2
Quadrics in affine and Euclidean spaces
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Subsection II.5.2.1
The general concept of a quadric
Subsection II.5.2.2
The center of a quadric
Subsection II.5.2.3
Canonical types of quadrics in affine space
Subsection II.5.2.4
General remarks on types of quadrics
Subsection II.5.2.5
Quadrics in Euclidean space
Section II.5.3
Projective spaces
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Subsection II.5.3.1
Models of the projective plane
Subsection II.5.3.2
Projective space of arbitrary dimension
Subsection II.5.3.3
Homogeneous coordinates
Subsection II.5.3.4
Affine maps
Subsection II.5.3.5
The concept of an algebraic variety
Subsection II.5.3.6
Projective group
Subsection II.5.3.7
Projective geometry
Subsection II.5.3.8
Cross-ratio
Subsection II.5.3.9
Expressions of cross-ratio in coordinates
Section II.5.4
Quadrics in projective space
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Subsection II.5.4.1
Classification
Subsection II.5.4.2
Examples and images of projective quadrics
Subsection II.5.4.3
Intersection of a line with a projective quadric
Subsection II.5.4.4
General remarks on projective quadrics