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Traits dedicated to linear algebra.
Traitsยง
- Affine
Space - A set points associated with a vector space and a transitive and free additive group action (the translation).
- Affine
Transformation - The group of affine transformations. They are decomposable into a rotation, a non-uniform scaling, a second rotation, and a translation (applied in that order).
- Direct
Isometry - Subgroups of the orientation-preserving isometry group
SE(n), i.e., rotations and translations. - Euclidean
Space - The finite-dimensional affine space based on the field of reals.
- Finite
DimInner Space - A finite-dimensional vector space equipped with an inner product that must coincide with the dot product.
- Finite
DimVector Space - A finite-dimensional vector space.
- Inner
Space - A vector space equipped with an inner product.
- Inversible
Square Matrix - The group of inversible matrix. Commonly known as the General Linear group
GL(n)by algebraists. - Isometry
- Subgroups of the isometry group
E(n), i.e., rotations, reflexions, and translations. - Matrix
- The space of all matrices.
- Matrix
Mut - The space of all matrices that are stable under modifications of its components, rows and columns.
- Normed
Space - A normed vector space.
- Orthogonal
Transformation - Subgroups of the n-dimensional rotations and scaling
O(n). - Projective
Transformation - The most general form of invertible transformations on an euclidean space.
- Rotation
- Subgroups of the n-dimensional rotation group
SO(n). - Scaling
- Subgroups of the (signed) uniform scaling group.
- Similarity
- Subgroups of the similarity group
S(n), i.e., rotations, translations, and (signed) uniform scaling. - Square
Matrix - The monoid of all square matrices, including non-inversible ones.
- Square
Matrix Mut - The monoid of all mutable square matrices that are stable under modification of its diagonal.
- Transformation
- A general transformation acting on an euclidean space. It may not be inversible.
- Translation
- Subgroups of the n-dimensional translation group
T(n). - Vector
Space - A vector space has a module structure over a field instead of a ring.