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Add explanation of basis concept in polynomials documentation #841

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2 changes: 1 addition & 1 deletion book/src/background/polynomials.md
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Expand Up @@ -218,7 +218,7 @@ over $\mathcal{H}.$

## Lagrange basis functions

> TODO: explain what a basis is in general (briefly).
In linear algebra, a **basis** is a set of linearly independent vectors that can be used to represent any vector in a given vector space through linear combinations. For the space of polynomials of degree at most $n-1$, a basis consists of $n$ linearly independent polynomials, and any polynomial in this space can be uniquely expressed as a linear combination of these basis polynomials.

Polynomials are commonly written in the monomial basis (e.g. $X, X^2, ... X^n$). However,
when working over a multiplicative subgroup of order $n$, we find a more natural expression
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