Symmetric power
In mathematics, the n-th symmetric power of an object X is the quotient of the n-fold product X n := X × ⋯ × X {\displaystyle X^{n}:=X\times \cdots \times X} by the permutation action of the symmetric group S n {\displaystyle {\mathfrak {S}}_{n}} . More precisely, the notion exists at least in the following three areas: In linear algebra, the 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 product).