Symmetric product information

Symmetric product may refer to: The product operation of a symmetric algebra The symmetric product of tensors The symmetric product of an algebraic curve...

a symmetric matrix is a square matrix that is equal to its transpose. Formally, A  is symmetric ⟺ A = A T . {\displaystyle A{\text{ is symmetric}}\iff...

In mathematics, the n-fold symmetric product of an algebraic curve C is the quotient space of the n-fold cartesian product C × C × ... × C or Cn by the...

For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The symmetric group is important to diverse areas of...

characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric algebra on V. A related concept is that of...

bilinear form to be symmetric if B(v, w) = B(w, v) for all v, w in V; alternating if B(v, v) = 0 for all v in V; skew-symmetric or antisymmetric if B(v...

basis of differential n-forms. The symmetric algebra is constructed in a similar manner, from the symmetric product: V ⊙ V := V ⊗ V / { v 1 ⊗ v 2 − v 2...

the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be...

theory of symmetric functions, as a concise relation between the generating series for elementary, complete and power sums homogeneous symmetric polynomials...

vectors Outer product The term scalar product means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms...

Generalized Symmetric Group", J. London Math. Soc. (2), 8, (1974), pp. 615–620 P. Graczyk, G. Letac and H. Massam, "The Hyperoctahedral Group, Symmetric Group...

identified with skew-symmetric matrices, so the product between a skew-symmetric matrix and vector is equivalent to the grade-1 part of the product of a bivector...

defined to be the symmetric map ⟨ x , y ⟩ = x y {\displaystyle \langle x,y\rangle =xy} (rather than the usual conjugate symmetric map ⟨ x , y ⟩ = x y...

the James reduced product is called the infinite symmetric product. James, I. M. (1955), "Reduced product spaces", Annals of Mathematics, Second Series,...

are semisimple symmetric spaces with G = H × H. Any semisimple symmetric space is a product of symmetric spaces of this form with symmetric spaces such that...

Boolean ring, with symmetric difference as the addition of the ring and intersection as the multiplication of the ring. The symmetric difference is equivalent...

which corresponds to embedding a symmetric power of a vector space into the symmetric elements of a tensor product of copies of it. The symbolic method...

{\displaystyle V} over a field F {\displaystyle F} with a symmetric bilinear form (the inner product, e.g. the Euclidean or Lorentzian metric) g : V × V →...

i<j\leq n} . This is invariant under the symmetric group, and Y {\displaystyle Y} is the quotient by the symmetric group of the non-excluded n {\displaystyle...

{\displaystyle \ M\ } is symmetric or Hermitian, and all its eigenvalues are real and positive.   M   {\displaystyle \ M\ } is symmetric or Hermitian, and all...

a symmetric polynomial if for any permutation σ of the subscripts 1, 2, ..., n one has P(Xσ(1), Xσ(2), ..., Xσ(n)) = P(X1, X2, ..., Xn). Symmetric polynomials...

n-th symmetric power of a vector space V is the vector subspace of the symmetric algebra of V consisting of degree-n elements (here the product is a tensor...

ordinary tensor product of modules), but not necessarily symmetric. If R is commutative, the category of left R-modules is symmetric monoidal. The latter...

displacement of the atomic positions leads to a loss of symmetry until the symmetric product re-forms (see image example below), where these displacements are...

matrix whose transpose is equal to itself is called a symmetric matrix; that is, A is symmetric if A T = A . {\displaystyle \mathbf {A} ^{\operatorname...