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Definition: Let

$(V,\langle \cdot,\cdot \rangle)$ be an inner product space. Let

$\vec{x},\vec{y} \in V$ . We say that

$\vec{x}$ and

$\vec{y}$ are orthogonal vectors if

$\langle \vec{x},\vec{y} \rangle = 0.$ Let

$S=\{v_1,v_2,\ldots\}$ be a set of vectors in

$V$ . We say that the set

$S$ is an orthogonal set of vectors if

$\langle v_n,v_m \rangle = 0$ for all

$m \neq n$ . Let

$(v_n)_{n=1}^{\infty}$ be a sequence of vectors in

$V$ . We say that the sequence

$(v_n)_{n=0}^{\infty}$ is an orthognal sequence of vectors if the set

$\{v_1,v_2,\ldots\}$ is an orthogonal set of vectors.

Definition: Consider an inner product space

$(\mathbb{P},\langle \cdot,\cdot \rangle)$ where

$\mathbb{P}$ denotes the set of all polynomials. The numbers

$m_n = \langle 1, x^n \rangle$ are called moments of the inner product space

$(\mathbb{P},\langle \cdot, \cdot \rangle)$ .