# arrow_back Show that $\langle v|A| w\rangle=\sum_{i j} A_{i j} v_{i}^{*} w_{j}$

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Show that $\langle v|A| w\rangle=\sum_{i j} A_{i j} v_{i}^{*} w_{j}$

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Let $V$ be the real vector space of continuous real-valued functions on the closed interval $[0,1]$, and let $w \in V$. For $p, q \in V$, define $\langle p, q\rangle=\int_{0}^{1} p(x) q(x) w(x) d x$.Let $V$ be the real vector space of continuous real-valued functions on the closed interval $0,1$, and let $w \in V$. For $p, q \in V$, defi ...
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An inner product on a real vector space $V$ is a function $\langle\cdot, \cdot\rangle: V \times V \rightarrow \mathbb{R}$ satisfying
An inner product on a real vector space $V$ is a function $\langle\cdot, \cdot\rangle: V \times V \rightarrow \mathbb{R}$ satisfyingAn inner product on a real vector space $V$ is a function $\langle\cdot, \cdot\rangle: V \times V \rightarrow \mathbb{R}$ satisfying ...
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Let $\mathcal{P}_{2}$ be the space of polynomials $p(x)=a+b x+c x^{2}$ of degree at most 2 with the inner product $\langle p, q\rangle=\int_{-1}^{1} p(x) q(x) d x$.
Let $\mathcal{P}_{2}$ be the space of polynomials $p(x)=a+b x+c x^{2}$ of degree at most 2 with the inner product $\langle p, q\rangle=\int_{-1}^{1} p(x) q(x) d x$.Let $\mathcal{P}_{2}$ be the space of polynomials $p(x)=a+b x+c x^{2}$ of degree at most 2 with the inner product $\langle p, q\rangle=\int_{-1}^ ... close 0 answers 11 views Let \(C[-1,1]$ be the real inner product space consisting of all continuous functions $f:[-1,1] \rightarrow \mathbb{R}$, with the inner product $\langle f, g\rangle:=\int_{-1}^{1} f(x) g(x) d x$.Let $C-1,1$ be the real inner product space consisting of all continuous functions $f:-1,1 \rightarrow \mathbb{R}$, with the inner product \(\ ...