In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning, such...

include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific...

parallel to the direction of displacement. This geometric transformation is a linear transformation of ⁠ R n {\displaystyle \mathbb {R} ^{n}} ⁠ that...

generalized in transformation geometry, which studies the properties of geometric objects that are preserved by different kinds of transformations. Classical...

metron meaning "measure". If the transformation is from a metric space to itself, it is a kind of geometric transformation known as a motion. Given a metric...

mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that...

geometry Infinitesimal transformation, a limiting case of a geometrical transformation Chemical transformation Phase transformation, a physical transition...

Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and...

Procrustes transformation is a geometric transformation that involves only translation, rotation, uniform scaling, or a combination of these transformations. Hence...

In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with the space of all directions...

a, b, c, d are complex numbers satisfying ad − bc ≠ 0. Geometrically, a Möbius transformation can be obtained by first applying the inverse stereographic...

Geometric transformations can be distinguished into two types: active or alibi transformations which change the physical position of a set of points relative...

number). Geometrically, vectors are multi-dimensional quantities with magnitude and direction, often pictured as arrows. A linear transformation rotates...

symmetries and geometric transformations: The symmetries of an object form a group, called the symmetry group of the object, and the transformations of a given...

pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them. It is opposed to...

when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation. In other contexts, it is analogous to...

time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects...

often possible to translate to and from eigenbases. Most common geometric transformations that keep the origin fixed are linear, including rotation, scaling...

also isotoxal. Duality is closely related to polar reciprocity, a geometric transformation that, when applied to a convex polyhedron, realizes the dual polyhedron...

Transformations of text are strategies to perform geometric transformations on text (reversal, rotations, etc.), particularly in systems that do not natively...

logical functions, and with the help of shifts it served also the geometric transformations—in short, it was doing all three types of the tasks (while other...

In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide")...

of techniques, including geometric transformations, color space adjustments, and noise injection. Geometric transformations alter the spatial properties...

In mathematics, a symmetry operation is a geometric transformation of an object that leaves the object looking the same after it has been carried out....

The Helmert transformation (named after Friedrich Robert Helmert, 1843–1917) is a geometric transformation method within a three-dimensional space. It...

spaces. A reflection across a hyperplane is a kind of motion (geometric transformation preserving distance between points), and the group of all motions...

)\end{bmatrix}}} Geometric transformation Improper rotation Linear transformation Orthogonal matrix Rigid transformation Unitary transformation Rowland, Todd...

generalize easily to A = P D P − 1 {\displaystyle A=PDP^{-1}} . The geometric transformation represented by a diagonalizable matrix is an inhomogeneous dilation...

unitary transformation U {\textstyle U} satisfies U U ∗ = I {\textstyle UU^{*}=I} . Taking the determinant ( N {\textstyle N} -th power of the geometric mean)...

In geometry, matrices are used for specifying and representing geometric transformations (for example rotations) and coordinate changes. In numerical analysis...