# Recent questions tagged metric

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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 $\ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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 8 views close 0 answers 6 views 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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What is a dot (inner) product?
What is a dot (inner) product?What is a dot (inner) product? ...
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Show that $\langle v|A| w\rangle=\sum_{i j} A_{i j} v_{i}^{*} w_{j}$
Show that $\langle v|A| w\rangle=\sum_{i j} A_{i j} v_{i}^{*} w_{j}$Show that $\langle v|A| w\rangle=\sum_{i j} A_{i j} v_{i}^{} w_{j}$ ...
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Let $f: N \rightarrow Y$ be a function defined as
Let $f: N \rightarrow Y$ be a function defined asLet $f: N \rightarrow Y$ be a function defined as $f(x)=4 x+3$ where $Y=\{y \in N: y=4 x+3$ for some $x \in N\}$ Show that $f$ is invertible and its i ...
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Let $f:(-1,1) \rightarrow B$, be a function defined by $f(x)=\tan ^{-1} \frac{2 x}{1-x^{2}}$, then $f$ is both one-one and onto when $B$ is the interval.
Let $f:(-1,1) \rightarrow B$, be a function defined by $f(x)=\tan ^{-1} \frac{2 x}{1-x^{2}}$, then $f$ is both one-one and onto when $B$ is the interval.Let $f:(-1,1) \rightarrow B$, be a function defined by $f(x)=\tan ^{-1} \frac{2 x}{1-x^{2}}$, then $f$ is both one-one and onto when $B$ is the interv ...
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Let $A$ and $B$ be metric spaces, and let $f: A \rightarrow B$. Suppose that whenever $X$ is an open set in $B$, the set $\{a \in A: f(a) \notin X\}$ is closed in $A .$ Which of the following must be true?Let $A$ and $B$ be metric spaces, and let $f: A \rightarrow B$. Suppose that whenever $X$ is an open set in $B$, the set $\{a \in A: f(a) \notin X\}$ ...
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Are all topological spaces metrizable?
Are all topological spaces metrizable?We say that a norm $|| \cdot ||$ generates a toplogy $\tau_{|| \cdot ||}$ if and only if $\tau_{|| \cdot ||}$ is the smallest tolpolgy in $X$ that con ...
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All metric spaces are topological spaces.
All metric spaces are topological spaces.Let $(X, || \cdot||)$ metrix space. Show that $(X, \tau_)$, where $\tau = \{ &nbsp;\mathcal{O} \subset X | &nbsp;\mathcal{O}\text{ is open with respec ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Calculate$\sin \left(\frac{\pi}{4}+i\right)$. 1 answer 65 views Calculate$\sin \left(\frac{\pi}{4}+i\right)$.Calculate$\sin \left(\frac{\pi}{4}+i\right)$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that$g \circ f$is a uniformly continuous function from$X$to$Z . \quad$1 answer 73 views Show that$g \circ f$is a uniformly continuous function from$X$to$Z . \quad$Let$f$be a uniformly continuous function from a metric space$X$to another metric space$Y$and$g$a uniformly continuous function from the metric ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let$\left\{p_{n}\right\}$be a sequence in a metric space. Give the definition of the convergence of this sequence. 1 answer 55 views Let$\left\{p_{n}\right\}$be a sequence in a metric space. Give the definition of the convergence of this sequence.Let$\left\{p_{n}\right\}$be a sequence in a metric space. Give the definition of the convergence of this sequence. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Give the equation for the$L^{p}$metric on$\mathbb{R}^{2}$. 1 answer 38 views Give the equation for the$L^{p}$metric on$\mathbb{R}^{2}$.Give the equation for the$L^{p}$metric on$\mathbb{R}^{2}$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Consider the sequence in$\mathbb{R}^{2}$given by $$x_{n}=\left(\frac{1}{n} \cos \left(\frac{\pi n}{2}\right), \frac{1}{n} \sin \left(\frac{\pi n}{2}\right)\right)$$ 1 answer 64 views Consider the sequence in$\mathbb{R}^{2}$given by $$x_{n}=\left(\frac{1}{n} \cos \left(\frac{\pi n}{2}\right), \frac{1}{n} \sin \left(\frac{\pi n}{2}\right)\right)$$Consider the sequence in$\mathbb{R}^{2}$given by$$x_{n}=\left(\frac{1}{n} \cos \left(\frac{\pi n}{2}\right), \frac{1}{n} \sin \left(\frac{\pi n}{2 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 An inner product on a real vector space$V$is a function$\langle\cdot, \cdot\rangle: V \times V \rightarrow \mathbb{R}$satisfying 1 answer 147 views 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 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What are normed spaces? 1 answer 51 views What are normed spaces?What are normed spaces? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 A metric on a set$S$is a function$d: S \times S \rightarrow \mathbb{R}$that satisfies 1 answer 53 views A metric on a set$S$is a function$d: S \times S \rightarrow \mathbb{R}$that satisfiesA metric on a set$S$is a function$d: S \times S \rightarrow \mathbb{R}\$ that satisfies ...
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What is a north-star online product metric?
What is a north-star online product metric?What is a north-star online product metric? ...
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Why do scientists prefer the SI units over the old English system of measurement?
Why do scientists prefer the SI units over the old English system of measurement?Why do scientists prefer the SI units over the old English system of measurement? ...
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Are SI units the same as metric units?
Are SI units the same as metric units?Are SI units the same as metric units? ...
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What is the most frequent metric to assess model accuracy for classification problems?