In mathematics, the symmetric algebra S(V) (also denoted Sym(V)) on a vector space V over a field K is a commutative algebra over K that contains V, and...

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

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group...

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 the...

S_{m}{\mathfrak {g}}} of symmetric tensor products Sym m ⁡ g {\displaystyle \operatorname {Sym} ^{m}{\mathfrak {g}}} . Its limit is the symmetric algebra S ( g ) {\displaystyle...

tensor algebra is important because many other algebras arise as quotient algebras of T(V). These include the exterior algebra, the symmetric algebra, Clifford...

In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its...

Pseudovector Spinor Tensor Tensor algebra, Free algebra Tensor contraction Symmetric algebra, Symmetric power Symmetric tensor Mixed tensor Pandey, Divyanshu;...

is the free anti-symmetric algebra over R {\displaystyle R} in n {\displaystyle n} -generators and the second ring is the free algebra over R {\displaystyle...

Multilinear algebra Symmetric algebra, the symmetric analog Tensor algebra Weyl algebra, a quantum deformation of the symmetric algebra by a symplectic...