Editing Tensor algebra (section)

==Non-commutative polynomials==
If ''V'' has finite dimension ''n'', another way of looking at the tensor algebra is as the "algebra of polynomials over ''K'' in ''n'' non-commuting variables". If we take [[basis vector]]s for ''V'', those become non-commuting variables (or [[Indeterminate (variable)|''indeterminates'']]) in ''T''(''V''), subject to no constraints beyond [[associativity]], the [[distributive law]] and ''K''-linearity.

Note that the algebra of polynomials on ''V'' is not <math>T(V)</math>, but rather <math>T(V^*)</math>: a (homogeneous) linear function on ''V'' is an element of <math>V^*,</math> for example coordinates <math>x^1,\dots,x^n</math> on a vector space are [[Covariant vector|covectors]], as they take in a vector and give out a scalar (the given coordinate of the vector).