# [−][src]Module alga::linear

Traits dedicated to linear algebra.

## Traits

 AffineSpace A set points associated with a vector space and a transitive and free additive group action (the translation). AffineTransformation 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). DirectIsometry Subgroups of the orientation-preserving isometry group `SE(n)`, i.e., rotations and translations. EuclideanSpace The finite-dimensional affine space based on the field of reals. FiniteDimInnerSpace A finite-dimensional vector space equipped with an inner product that must coincide with the dot product. FiniteDimVectorSpace A finite-dimensional vector space. InnerSpace A vector space equipped with an inner product. InversibleSquareMatrix 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. MatrixMut The space of all matrices that are stable under modifications of its components, rows and columns. NormedSpace A normed vector space. OrthogonalTransformation Subgroups of the n-dimensional rotations and scaling `O(n)`. ProjectiveTransformation 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. SquareMatrix The monoid of all square matrices, including non-inversible ones. SquareMatrixMut 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)`. VectorSpace A vector space has a module structure over a field instead of a ring.