Linear mapIn mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .
Affine transformationIn Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles. More generally, an affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space onto itself while preserving both the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments.
Dynamics (music)In music, the dynamics of a piece are the variation in loudness between notes or phrases. Dynamics are indicated by specific musical notation, often in some detail. However, dynamics markings require interpretation by the performer depending on the musical context: a specific marking may correspond to a different volume between pieces or even sections of one piece. The execution of dynamics also extends beyond loudness to include changes in timbre and sometimes tempo rubato. Dynamics are one of the expressive elements of music.
