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