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Rotation matrix

In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix rotates points in the xy plan

Translation (geometry)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted a

Glide reflection

In 2-dimensional geometry, a glide reflection (or transflection) is a symmetry operation that consists of a reflection over a line and then translation along that line, combined into a single operatio

Response modeling methodology

Response modeling methodology (RMM) is a general platform for statistical modeling of a linear/nonlinear relationship between a response variable (dependent variable) and a linear predictor (a linear

Geometric transformation

In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and

Translation of axes

In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k

Transformation matrix

In linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation

Homothety

In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number k called its ratio, which send

Linear map

In 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

Scaling (geometry)

In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions. Th

Infinitesimal transformation

In mathematics, an infinitesimal transformation is a limiting form of small transformation. For example one may talk about an infinitesimal rotation of a rigid body, in three-dimensional space. This i

Householder transformation

In linear algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection about a plane or hyperplane cont

Motion (geometry)

In geometry, a motion is an isometry of a metric space. For instance, a plane equipped with the Euclidean distance metric is a metric space in which a mapping associating congruent figures is a motion

Affine transformation

In 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 Euclidea

Rotation of axes

In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes

Late-stage functionalization

Late-stage functionalization (LSF) is a desired, chemical or biochemical, chemoselective transformation on a complex molecule to provide at least one analog in sufficient quantity and purity for a giv

Helmert transformation

The Helmert transformation (named after Friedrich Robert Helmert, 1843–1917) is a geometric transformation method within a three-dimensional space. It is frequently used in geodesy to produce datum tr

Homography

In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive. It is a bijection that maps lines t

Vector projection

The vector projection of a vector a on (or onto) a nonzero vector b, sometimes denoted (also known as the vector component or vector resolution of a in the direction of b), is the orthogonal projectio

Locally finite operator

In mathematics, a linear operator is called locally finite if the space is the union of a family of finite-dimensional -invariant subspaces. In other words, there exists a family of linear subspaces o

Reflection (mathematics)

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dime

Transformation (function)

In mathematics, a transformation is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f : X → X.Examples include linear transformations of vector spaces and g

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