N-graded Vector Spaces
Let be the set of non-negative integers. An -graded vector space, often called simply a graded vector space without the prefix, is a vector space V which decomposes into a direct sum of the form
where each is a vector space. For a given n the elements of are then called homogeneous elements of degree n.
Graded vector spaces are common. For example the set of all polynomials in one variable form a graded vector space, where the homogeneous elements of degree n are exactly the linear combinations of monomials of degree n.
Read more about this topic: Graded Vector Space
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