Editing Quotient space (linear algebra) (section)

===Polynomial Vector Space===

Let <math>\mathcal{P}_3(\mathbb{R})</math> be the vector space of all cubic polynomials over the real numbers. Then <math>\mathcal{P}_3(\mathbb{R}) / \langle x^2 \rangle </math> is a quotient space, where each element is the set corresponding to polynomials that differ by a quadratic term only. For example, one element of the quotient space is <math>\{x^3 + a x^2 - 2x + 3 : a \in \mathbb{R}\}</math>, while another element of the quotient space is <math>\{a x^2 + 2.7 x : a \in \mathbb{R}\}</math>.