Recent questions tagged metric

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Why is EBITDA important for Businesses?

asked May 23 in Accounting & Tax by ♦MathsGee Platinum (93,212 points) | 20 views

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What is EBITDA?

asked May 23 in Accounting & Tax by ♦MathsGee Platinum (93,212 points) | 23 views

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How do I choose the right evaluation metric for my model?

asked Dec 21, 2022 in Data Science & Statistics by ♦MathsGee Platinum (93,212 points) | 119 views

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Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that

asked Sep 23, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 87 views

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Find all functions $f$ such that \[ f(f(x)+y)=f\left(x^2-y\right)+4 y f(x) \] for all real numbers $x$ and $y$.

asked Sep 23, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 113 views

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Find all functions $f$ from $\mathbb{R} \backslash\{0\}$ to itself satisfying \[ f(x)+f(y)=f(x y f(x+y)) \] for all $x, y \neq 0$ with $x+y \neq 0$.

asked Sep 23, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 77 views

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Find all functions $f: \mathbb{Q} \rightarrow \mathbb{Q}$ such that

asked Sep 22, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 93 views

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Determine all functions $f: \mathbb{Q} \rightarrow \mathbb{Q}$ such that \[ f(x f(y))=(1-y) f(x y)+x^2 y^2 f(y) \] holds for all real numbers $x$ and $y$.

asked Sep 22, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 86 views

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Find all functions $f: \mathbb{N}_0 \rightarrow \mathbb{N}_0$ whose minimum value is 1 and $f(f(n))=f(n)+1 \quad$ for all $n \in \mathbb{N}_0$

asked Sep 22, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 85 views

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Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that for all $x, y$ \[ f\left(x^2\right)-f\left(y^2\right)=(x+y)(f(x)-f(y)) . \]

asked Sep 22, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 110 views

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Does there exist a function $f: \mathbb{N}_0 \rightarrow \mathbb{N}_0$ such that

asked Sep 22, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 81 views

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Find all functions $f: \mathbb{N}_0 \rightarrow \mathbb{N}_0$ satisfying $f(2)=2, f(n)<f(n+1)$ and $f(m n)=$ $f(m) f(n)$ for all $m, n \in \mathbb{N}$

asked Sep 22, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 66 views

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What is the formula for flow rate $Q$ ?

asked Jul 29, 2022 in General Knowledge by ♦GaussTheBot Diamond (50,323 points) | 185 views

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Let $f$ and $g$ be continuous mappings of a metric space $X$ into a metric space $Y$, and let $E$ be a dense subset of $X$. Prove that $f(E)$ is dense in $f(X)$.

asked Jul 5, 2022 in Mathematics by ♦GaussTheBot Diamond (50,323 points) | 181 views

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Let $f$ be a continuous real function on a metric space $X$. Let $Z(f)$ (the zero set of $f$ ) be the set of all $p \in X$ at which $f(p)=0$. Prove that $Z(f)$ is closed.

asked Jul 5, 2022 in Mathematics by ♦GaussTheBot Diamond (50,323 points) | 222 views

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If $f$ is a continuous mapping of a metric space $X$ into a metric space $Y$, prove that \[ f(\bar{E}) \subset \overline{f(E)} \] for every set $E \subset X$. ( $\bar{E}$ denotes the closure of $E$.

asked Jul 5, 2022 in Mathematics by ♦GaussTheBot Diamond (50,323 points) | 168 views

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Let $X$ be a metric space, with metric $d$. Fix a point $a \in X$. Assign to each $p \in X$ the function $f_{p}$ defined by \[ f_{p}(x)=d(x, p)-d(x, a) \quad(x \in X) . \]

asked Jul 5, 2022 in Mathematics by ♦GaussTheBot Diamond (50,323 points) | 126 views

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Prove that \[ \sum_{i} \sum_{j} a_{i j}=-2, \quad \sum_{j} \sum_{i}=0 . \]

asked Jul 5, 2022 in Mathematics by ♦GaussTheBot Diamond (50,323 points) | 126 views

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Is $g$ continuous?

asked Jul 5, 2022 in Mathematics by ♦GaussTheBot Diamond (50,323 points) | 120 views

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Consider the motions of non-sero-rest-mass particles in a gravitional field created by a mass $M$ and characterized by the Schwarzschild metric

asked Jul 1, 2022 in Mathematics by ♦GaussTheBot Diamond (50,323 points) | 90 views

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In soccer analytics, what is the possession value metric?

asked Apr 10, 2022 in General Knowledge by ♦MathsGee Platinum (93,212 points) | 219 views

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In soccer analytics, what does the goalkeeper expected goals metric measure?

asked Apr 10, 2022 in General Knowledge by ♦MathsGee Platinum (93,212 points) | 249 views

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What does the brand penetration share metric measure?

asked Feb 16, 2022 in General Knowledge by ♦GaussTheBot Diamond (50,323 points) | 237 views

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How does time period measured for a given metric affect the signal-to-noise ratio?

asked Feb 16, 2022 in General Knowledge by ♦GaussTheBot Diamond (50,323 points) | 210 views

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When is a metric useful?

asked Feb 16, 2022 in General Knowledge by ♦GaussTheBot Diamond (50,323 points) | 209 views

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What Is a Metric?

asked Feb 16, 2022 in General Knowledge by ♦GaussTheBot Diamond (50,323 points) | 354 views

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Let $v_{1} \ldots v_{k}$ be vectors in a linear space with an inner product $\langle,$,$rangle . Define the$ Gram determinant by $G\left(v_{1}, \ldots, v_{k}\right)=\operatorname{det}\left(\left\langle v_{i}, v_{j}\right\rangle\right)$.

asked Jan 21, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 279 views

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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 $\langle f, g\rangle:=\int_{-1}^{1} f(x) g(x) d x$.

asked Jan 21, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 338 views

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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 $\langle p, q\rangle=\int_{-1}^{1} p(x) q(x) d x$.

asked Jan 21, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 185 views

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Let $w(x)$ be a positive continuous function on the interval $0 \leq x \leq 1, n$ a positive integer, and $\mathcal{P}_{n}$ the vector space of polynomials $p(x)$ whose degrees are at most $n$ equipped with the inner product

asked Jan 21, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 283 views

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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 $\langle p, q\rangle=\int_{0}^{1} p(x) q(x) w(x) d x$.

asked Jan 21, 2022 in Mathematics by ♦MathsGee Platinum (93,212 points) | 223 views

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What is a dot (inner) product?

asked Aug 9, 2021 in Mathematics by ♦Maths Genie Bronze Status (8,772 points) | 256 views

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

asked Jul 24, 2021 in Mathematics by ♦MathsGee Platinum (93,212 points) | 232 views

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Let $f: N \rightarrow Y$ be a function defined as

asked Jun 9, 2021 in Mathematics by ♦MathsGee Platinum (93,212 points) | 214 views

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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.

asked Jun 9, 2021 in Mathematics by ♦MathsGee Platinum (93,212 points) | 280 views

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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?

asked May 30, 2021 in Mathematics by ♦MathsGee Platinum (93,212 points) | 193 views

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Are all topological spaces metrizable?

asked May 11, 2021 in Mathematics by Sabelo Letsoalo (25 points) | 197 views

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All metric spaces are topological spaces.

asked May 11, 2021 in Mathematics by Sabelo Letsoalo (25 points) | 184 views

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Calculate $\sin \left(\frac{\pi}{4}+i\right)$.

asked May 10, 2021 in Mathematics by ♦GaussTheBot Diamond (50,323 points) | 254 views

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Show that $g \circ f$ is a uniformly continuous function from $X$ to $Z . \quad$

asked May 10, 2021 in Mathematics by Student Bronze Status (5,672 points) | 281 views

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Let $\left\{p_{n}\right\}$ be a sequence in a metric space. Give the definition of the convergence of this sequence.

asked May 10, 2021 in Mathematics by Student Bronze Status (5,672 points) | 284 views

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Give the equation for the $L^{p}$ metric on $\mathbb{R}^{2}$.

asked May 10, 2021 in Mathematics by Student Bronze Status (5,672 points) | 172 views

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Consider the sequence in $\mathbb{R}^{2}$ given by $$ x_{n}=\left(\frac{1}{n} \cos \left(\frac{\pi n}{2}\right), \frac{1}{n} \sin \left(\frac{\pi n}{2}\right)\right) $$

asked May 10, 2021 in Mathematics by Student Bronze Status (5,672 points) | 252 views

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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

asked May 8, 2021 in Mathematics by ♦GaussTheBot Diamond (50,323 points) | 753 views

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What are normed spaces?

asked May 8, 2021 in Mathematics by ♦GaussTheBot Diamond (50,323 points) | 204 views

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A metric on a set $S$ is a function $d: S \times S \rightarrow \mathbb{R}$ that satisfies

asked May 8, 2021 in Mathematics by ♦GaussTheBot Diamond (50,323 points) | 200 views

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What is a north-star online product metric?

asked Mar 25, 2021 in Data Science & Statistics by ♦MathsGee Platinum (93,212 points) | 233 views

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Why do scientists prefer the SI units over the old English system of measurement?

asked Sep 15, 2020 in General Knowledge by ♦MathsGee Platinum (93,212 points) | 285 views

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Are SI units the same as metric units?

asked Sep 15, 2020 in General Knowledge by ♦MathsGee Platinum (93,212 points) | 282 views

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What is the most frequent metric to assess model accuracy for classification problems?

asked Aug 2, 2020 in Data Science & Statistics by ♦MathsGee Platinum (93,212 points) | 283 views

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