Traits dedicated to linear algebra.
A set points associated with a vector space and a transitive and free additive group action (the translation).
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).
Subgroups of the orientation-preserving isometry group
The finite-dimensional affine space based on the field of reals.
A finite-dimensional vector space equipped with an inner product that must coincide with the dot product.
A finite-dimensional vector space.
A vector space equipped with an inner product.
The group of inversible matrix. Commonly known as the General Linear group
Subgroups of the isometry group
The space of all matrices.
The space of all matrices that are stable under modifications of its components, rows and columns.
A normed vector space.
Subgroups of the n-dimensional rotations and scaling
The most general form of inversible transformations on an euclidean space.
Subgroups of the n-dimensional rotation group
Subgroups of the (signed) uniform scaling group.
Subgroups of the similarity group
The monoid of all square matrices, including non-inversible ones.
The monoid of all mutable square matrices that are stable under modification of its diagonal.
A general transformation acting on an euclidean space. It may not be inversible.
Subgroups of the n-dimensional translation group
A vector space has a module structure over a field instead of a ring.