n
(geometry, linear algebra) A geometric transformation that preserves lines and parallelism, but in general not lengths or angles; (more formally) an automorphism of an affine space: a mapping of an affine space onto itself that preserves both the dimension of any affine subspace and the ratio of the lengths of any pair of parallel line segments.
n
(geometry) An automorphism of affine space.
adj
(mathematics) affine in most respects
n
(topology) The quality of a Hausdorff space of being angelic.
n
(linear algebra) The diagonal of a matrix that leads from top-right towards bottom-left.
adj
(mathematics) Such that the canonical mapping is injective.
n
(mathematics) a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included
n
(mathematics) An isometry of a metric space to itself
n
(algebra) An isomorphism of a mathematical object or system of objects onto itself.
n
(mathematics) The property of being automorphic.
adj
(mathematics) Of a monoidal category: both left-closed and right-closed.
n
(mathematics) A squared normalised form of a bispectrum.
n
(mathematics) A bijective holomorphism whose inverse is also holomorphic
n
(mathematics) Synonym of bimonoid
n
(algebraic topology) A homomorphism that operates on the kth boundary element.
n
Synonym of d'Alembert operator
n
(algebraic geometry) A kind of manifold having properties, such as Ricci flatness, that yield applications in theoretical physics.
n
(mathematics) A particular system of covectors.
adj
(mathematics) homomorphic and free
n
(mathematics) The dual of a homotopy.
n
(mathematics) The dual of a monoid
adj
(mathematics) Relating to a comonoid
n
(mathematics) A complex number.
adj
(mathematics) Being the dual of a natural entity.
adj
(mathematics) Describing a pair of contact manifolds that have a diffeomorphism
adj
(obsolete) Of or relating to algebra.
n
(mathematics) The vector space which comprises the set of continuous linear functionals of a given topological vector space.
n
(mathematics) A form of tensor in which each position is associated with two possible bases
n
(mathematics) A cobordism between a manifold and itself.
adj
(mathematics, chemistry) Perfectly ordered
adj
(mathematics) Pertaining to Galois theory.
n
(mathematics) A form of bilinear invariant
n
(physics, classical mechanics) One of the equations/identities which define a variety within the configuration space, such that the state of the physical system being described is constrained to correspond only to points within that variety.
n
(geometry) An element of a homaloidal system, in particular the image of a hyperplane under a Cremona transformation.
n
(mathematics) The formation of a new graph by inserting new nodes along existing edges.
n
(topology, algebraic topology) A general way of associating a sequence of algebraic objects, such as abelian groups or modules, to a sequence of topological spaces; also used attributively: see Usage notes below.
adv
(mathematics) By means of a homomorphism.
n
(algebra) A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces.
adj
(mathematics, geometry) for a geometric figure that is the image of another figure under an homothety.
n
(mathematics) The dual of a hyperhomology.
n
(mathematics) A function between metric spaces (or on a single metric space) having the property that the distance between two images is equal to the distance between their preimages.
n
(group algebra) A bijection f such that both f and its inverse f⁻¹ are homomorphisms, that is, structure-preserving mappings.
n
(mathematics) A form of vector associated with isospin
n
(mathematics) A nonassociative generalization of a groupoid
adj
(mathematics) Describing a lattice with the property that its every orthogonal pair is modular.
n
(mathematics) Having the property that every open cover has an open refinement that is locally finite.
adj
(mathematics, of a square matrix, now more commonly) Symmetrical about the anti-diagonal.
n
(mathematics) An element of a matrix that is used as a focus for row operations, such as dividing the row by the pivot, or adding multiples of the row to other rows making all other values in the pivot column 0.
adj
(mathematics) Having the property that the inverse systems of the Koszul cohomology modules satisfy the Inverse limit#Mittag-Leffler condition.)
adj
(mathematics) Being the holomorphic part of an almost holomorphic modular form.
n
(differential geometry) A process that deforms the metric of a Riemannian manifold in a way formally analogous to the diffusion of heat, smoothing out irregularities in the metric.
n
(mathematics) A bijective correspondence between permutations and pairs of standard Young tableaux of the same shape. It has applications in combinatorics and other areas.
n
(topology) Any of the pieces that constitute an order tree.
adj
(mathematics, in projective geometry) Of a proposition that is equivalent to its dual.
n
(mathematics) A nonassociative generalization of a semigroupoid
adj
(mathematics) Describing a conformal algebra related to supersymmetry
adj
(mathematics) Describing a space group in which all symmetry operations (apart from translation) leave one common point in a fixed location
adj
(mathematics, multilinear algebra, of a vector space) That is equipped with an alternating nondegenerate bilinear form.
n
(linear algebra) For given field F (especially the real numbers), even order 2n and nonsingular skew-symmetric matrix Ω, any 2n×2n matrix M with elements in F such that MᵀΩM = Ω (where Mᵀ denotes the transpose of M).
n
(mathematics) An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure.
n
(mathematics) A totally-ordered monoid
adj
(linear algebra, of a matrix) Having nonzero elements only in the main diagonal and the diagonals directly above and below it
adj
(mathematics) Such that every isomorphism between finitely generated substructures extends to an automorphism of itself.
adj
(mathematics) Isomorphic to a countable direct limit of matricial algebras.
n
(quaternion algebra) A quaternion of norm one.
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