even isometry
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Euclidean plane isometry — In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length. There are four types: translations, rotations, reflections,… … Wikipedia
Point groups in three dimensions — In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries… … Wikipedia
Dihedral group — This snowflake has the dihedral symmetry of a regular hexagon. In mathematics, a dihedral group is the group of symmetries of a regular polygon, including both rotations and reflections.[1] Dihedr … Wikipedia
Conjugation of isometries in Euclidean space — In a group, the conjugate by g of h is ghg−1. Contents 1 Translation 2 Inversion 3 Rotation 4 Reflection … Wikipedia
Point groups in two dimensions — In geometry, a point group in two dimensions is an isometry group in two dimensions that leaves the origin fixed, or correspondingly, an isometry group of a circle. It is a subgroup of the orthogonal group O(2), the group of all isometries which… … Wikipedia
Euclidean group — In mathematics, the Euclidean group E ( n ), sometimes called ISO( n ) or similar, is the symmetry group of n dimensional Euclidean space. Its elements, the isometries associated with the Euclidean metric, are called Euclidean moves.These groups… … Wikipedia
Metric space — In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3 dimensional Euclidean… … Wikipedia
Itō calculus — Itō calculus, named after Kiyoshi Itō, extends the methods of calculus to stochastic processes such as Brownian motion (Wiener process). It has important applications in mathematical finance and stochastic differential equations.The central… … Wikipedia
Polar decomposition — In mathematics, particularly in linear algebra and functional analysis, the polar decomposition of a matrix or linear operator is a factorization analogous to the polar form of a nonzero complex number z where r is the absolute value of z (a… … Wikipedia
Rotation matrix — In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix rotates points in the xy Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian… … Wikipedia
Quadratic form — In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example, is a quadratic form in the variables x and y. Quadratic forms occupy a central place in various branches of mathematics, including… … Wikipedia
