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Definition of the orthogonal group
...
Area of mathematics
Geometry
Differential geometry
Lie group
Important Lie group
Orthogonal group
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words: 281
articles: 5
Intuitive definition: real group of rotations + reflections.
Mathematical definition that most directly represents this:
the orthogonal group is the group of all matrices that preserve the dot product
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Table of contents
281
5
The orthogonal group is the group of all matrices that preserve the dot product
Definition of the orthogonal group
160
1
What happens to the definition of the orthogonal group if we choose other types of symmetric bilinear forms
The orthogonal group is the group of all matrices that preserve the dot product
104
The orthogonal group is the group of all invertible matrices where the inverse is equal to the transpose
Definition of the orthogonal group
82
1
Elements of the orthogonal group have determinant plus or minus one
The orthogonal group is the group of all invertible matrices where the inverse is equal to the transpose
The orthogonal group is the group of all matrices with orthonormal rows and orthonormal columns
Definition of the orthogonal group
23
Ancestors
(8)
Orthogonal group
Important Lie group
Lie group
Differential geometry
Geometry
Area of mathematics
Mathematics
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