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.