# [−][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 |

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 |

Isometry | Subgroups of the isometry group |

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 |

ProjectiveTransformation | The most general form of invertible transformations on an euclidean space. |

Rotation | Subgroups of the n-dimensional rotation group |

Scaling | Subgroups of the (signed) uniform scaling group. |

Similarity | Subgroups of the similarity group |

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 |

VectorSpace | A vector space has a module structure over a field instead of a ring. |