Recent questions tagged metric

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What is a dot (inner) product?
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What is a dot (inner) product?What is a dot (inner) product? ...
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Show that $\langle v|A| w\rangle=\sum_{i j} A_{i j} v_{i}^{*} w_{j}$
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Show that $\langle v|A| w\rangle=\sum_{i j} A_{i j} v_{i}^{*} w_{j}$Show that $\langle v|A| w\rangle=\sum_{i j} A_{i j} v_{i}^{} w_{j}$ ...
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Let $f: N \rightarrow Y$ be a function defined as
1 answer 43 views
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.
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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 interv ...
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0 answers 29 views
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?
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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.
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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\}$be a sequence in a metric space. Give the definition of the convergence of this sequence. 1 answer 54 views Let$\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 143 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 52 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?
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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?
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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? ...
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Are SI units the same as metric units?
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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?
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What is the most frequent metric to assess model accuracy for classification problems?What is the most frequent metric to assess model accuracy for classification problems? ...
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Why is Area Under ROC Curve (AUROC) better than raw accuracy as an out-of- sample evaluation metric?
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Why is Area Under ROC Curve (AUROC) better than raw accuracy as an out-of- sample evaluation metric?Why is Area Under ROC Curve (AUROC) better than raw accuracy as an out-of- sample evaluation metric? ...
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Why is EBITDA important as a business metric (KPI)?
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Why is EBITDA important as a business metric (KPI)?Why is EBITDA important as a business metric (KPI)? ...
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How do you measure risk? Can you give an example of a specific metric that measures information security risk?
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How do you measure risk? Can you give an example of a specific metric that measures information security risk?How do you measure risk? Can you give an example of a specific metric that measures information security risk? ...
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