adj
(mathematics) Of a binary function, commutative.
n
(mathematics) The transpose of the cofactor matrix of a given square matrix.
adj
(mathematics) That may be made adjoint
n
(mathematics) The transpose of the respective cofactor matrix, for a given matrix. One of the factors in calculating the inverse of a matrix. Commonly notated as adj(A), where A is the given matrix.
adj
(mathematics, not comparable) Of or relating to the inverse bundle corresponding to a canonical bundle.
adj
(algebra) Of an operator * for which a * b = - (b * a)
adj
(mathematics) Having the property that when subjected to a specified operation the result is the same as multiplying by the determinant.
n
(mathematics) An orthomodular lattice in which a ∨ b = 1 for any a, b ≠ 0.
adj
(of a matrix) Whose transpose equals its negative (i.e., Mᵀ = −M);
n
(mathematics) Any antiunitary operator
n
(mathematics, category theory) An equivalence between an object and itself.
adj
(mathematics) adjoint in two different ways
n
(mathematics) A biadjoint adjunction
n
(mathematics) The process that makes a category bicomplete
adj
(mathematics, of two entities A and B) Both left equivalent and right equivalent; Having the property that there exists a pair of mappings M₁ (A->B) and M₂ (B->A) such that M₁M₂(A) is equivalent to applying the unity operator to A and M₂ M₁(B) is equivalent to applying the unity operator to B.
n
(mathematics) A transform used in Borel summation.
adj
(mathematics) Describing the dual of an adjoint representation
n
(cohomology) A cochain that is in the kernel of a coboundary map.
n
(mathematics) Adjoint; The transposed matrix of the cofactors of the entries of a matrix.
n
(algebra, logic) The subset of all elements of a semigroup that commute with the elements of a given subset
adj
(mathematics, of a binary operation) Such that the order in which the operands are taken does not affect their image under the operation.
n
(mathematics) A mapping associated with a morphism that, when applied to every member of the morphism, results in the same value as the morphism applied to the image of every member.
adj
(mathematics) Of a representation in linear algebra: being the transpose of the former representation of an inverse object.
adj
(functional analysis, not comparable, of a real-valued function on the reals) having an epigraph that is a convex set.
n
(mathematics) A comodule.
n
(mathematics) An object in a comodule or other dual to an abelian object that has a specified property.
n
(mathematics) An equivalence map that is the dual of a translation.
n
(linear algebra) A vector product.
n
The complement of a union is the intersection of the complements; as expressed by: (𝐴 ∪ 𝐵)′ = 𝐴′ ∩ 𝐵′
n
(mathematics) Field dealing with differentiable functions on differentiable manifolds.
adj
(mathematics, of a family of functions) Such that all members are continuous, with equal variation in a given neighborhood.
n
(linear algebra) A square matrix with constant skew-diagonals (positive sloping diagonals).
adj
(mathematics, of an operator) Equal to its own transpose conjugate.
n
(linear algebra) transpose conjugate
adj
(complex analysis, of a complex function) Complex-differentiable on an open set around every point in its domain.
n
(mathematics) section through a hypersurface
adj
(mathematics) (said of a binary operation) Such that all of the distinct elements it can operate on are idempotent (in the sense given just above).
n
(linear algebra) A function or property of a matrix, defined as a generalization of the concepts of determinant and permanent.
n
(mathematics) A smooth map whose differential is everywhere injective, related to the mathematical concept of an embedding.
n
The set of points that map to a given point (or set of points) under a specified function.
n
(mathematics) Given two matrices M, N of order w, the involutant is the resultant of the w² scalar equations obtained by equating to zero a linear function with scalar coefficients of the w² matrices which result from multiplying 1, m m², ... mʷ⁻¹ into 1, n, n², ... nʷ⁻¹.
n
(computer science) a one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets
n
(mathematics) Given a binary operation × defined on a set S which also has additive operation + and additive identity 0, the property that a × (b×c) + b × (c×a) + c × (a×b) = 0 for all a, b, c in S.
n
(mathematics) A Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a generalized Cartan matrix. They have applications in theoretical physics.
n
(topology, Lie theory) A discrete subgroup L of a given locally compact group G whose quotient space G/L has finite invariant measure.
adj
(mathematics) Describing an associative monoidal functor.
adj
(linear algebra) (Of a set of vectors or ring elements) whose nontrivial linear combinations are nonzero
n
(linear algebra) A matrix decomposition which writes a matrix as the product of a lower and upper triangular matrix, used in numerical analysis to solve systems of linear equations or find the inverse of a matrix.
adj
(mathematics) Of a polynomial whose leading coefficient is one.
n
(mathematics) an injective homomorphism
n
(mathematics) A certain relationship defined between algebraic rings that preserves many ring-theoretic properties.
n
Alternative letter-case form of Noetherian module [(algebra) A module whose every submodule is finitely generated; or equivalently, a module whose submodules satisfy an ascending chain condition (i.e., any ascending chain of submodules levels off after a finite number of steps).]
n
(algebra) An algebra over a ring whose bilinear product is not necessarily associative.
adj
(mathematics) Not selfadjoint
n
(geometry, group theory) The subset of elements of a set X to which a given element can be moved by members of a specified group of transformations that act on X.
n
(mathematics) Property of a certain category of graphs.
n
(mathematical analysis) A kind of linear functional which yields a non-negative scalar when given a non-negative function as parameter.
n
(mathematics) An extension of the differential operator, used in the theory of partial differential equations and quantum field theory.
n
2015, Jyoti Prakash Saha, “Variation of Weyl modules in p-adic families”, in arXiv:
adj
(mathematics) Describing a matrix, all of whose elements are nonnegative except for those on the main diagonal
n
(mathematics) A Schur polynomial.
n
(linear algebra) Cauchy-Schwarz inequality
adj
(mathematics) Adjoint to itself.
n
(mathematics) Given a bounded linear operator B and its adjoint B*, the self-commutator is B*B - BB*.
adj
Alternative spelling of self-adjoint [(mathematics) Adjoint to itself.]
adj
(mathematics, of an algebraic group) Being a linear algebraic group whose radical of the identity component is trivial.
adj
(mathematics, linear algebra) Of two square matrices; being such that a conjugation sends one matrix to the other.
n
(mathematics) Synonym of singleton (“a set containing exactly one element”)
adj
(linear algebra, of matrix) Having no inverse.
n
(linear algebra) A square matrix which is not invertible.
adj
(linear algebra) of a matrix T, such that T^†=-T
n
(linear algebra, probability theory, statistics) A matrix having the property that the entries in each column are non-negative, real and sum to 1.
n
(mathematics) A differentiable map whose differential is everywhere surjective.
adj
(mathematics) Having the property that it is the quotient of a projective module by a projective submodule, having an ext functor with itself of 0, and there being a right module as the kernel of a surjective morphism between finite direct sums of its direct summands.
adj
(mathematics, of a lattice or matrix) Having a determinant of 1 or -1.
adj
(mathematics, linear algebra, mathematical analysis, of a matrix or operator) Whose inverse is equal to its adjoint.
adj
(of a real-valued function on a topological space) Such that for each fixed point x there is some neighborhood whose image's limit superior is x's image.
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