Question

Explain tensor algebra quotient law, addition, and subtraction of tensor.
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Answer 1

Answer:

Algebra tensor - In mathematics, the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product. ... The tensor algebra is important because many other algebras arise as quotient algebras of T(V).

Addition tensor- In mathematics, a tensor is an algebraic object that describes a (multilinear) relationship between sets of algebraic objects related to a vector space. Objects that tensors may map between include vectors and scalars, and even other tensors. Tensors can take several different forms – for example: scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system.

Answer 2

Answer:

Explain tensor algebra quotient law, addition, and subtraction of tensor.