Razlika između inačica stranice »Metrika«
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|obrađivač=Zoran Škoda | |obrađivač=Zoran Škoda | ||
|faza_obrade=zaključaj naziv | |faza_obrade=zaključaj naziv | ||
| − | |definicija=funkcija | + | |definicija=[[funkcija]] <math> d</math> na skupu <math> X</math> koja svakomu paru točaka <math> (x,y)</math> pridružuje [[nenegativni realni broj]] <math> d(x,y)</math> koji je [[nula]] [[ako i samo ako]] je <math> x=y</math> i koja zadovoljava [[simetrična funkcija|simetriju]] <math> d(x,y)=d(y,x)</math> i [[nejednakost trokuta]] <math>d(x,y)+d(y,z) \geqslant d(x,z)</math> |
|skolska_definicija= | |skolska_definicija= | ||
|napomena= | |napomena= | ||
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|naziv=metric | |naziv=metric | ||
|klasifikacija=Calculus and Analysis > Differential Geometry > Metrics > | |klasifikacija=Calculus and Analysis > Differential Geometry > Metrics > | ||
| − | |definicija= A nonnegative function | + | |definicija= A [[nenegativna funkcija|nonnegative function]] <math> g(x,y)</math> describing the "distance" between neighboring points for a given set. A '''metric''' satisfies the [[relacija trokuta|triangle inequality]] |
| − | + | <math>g(x,y)+g(y,z)>=g(x,z)</math> (1) | |
| − | and is symmetric, so | + | and is [[simetrična funkcija|symmetric]], so |
| − | + | <math>g(x,y)=g(y,x)</math> (2) | |
A metric also satisfies | A metric also satisfies | ||
| − | + | <math>g(x,x)=0</math>, (3) | |
| − | as well as the condition that | + | as well as the condition that <math>g(x,y)=0</math> implies <math>x=y</math>. |
|cite=Weisstein, Eric W. "Metric." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Metric.html | |cite=Weisstein, Eric W. "Metric." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Metric.html | ||
| − | |napomena=If this latter condition is dropped, then | + | |napomena=If this latter condition is dropped, then <math> g(x,y)</math> is called a [[pseudometrika|pseudometric]] instead of a metric. |
| − | A set possessing a metric is called a metric space. When viewed as a tensor, the metric is called a metric tensor. | + | A set possessing a metric is called a [[metrički prostor|metric space]]. When viewed as a [[tenzor|tensor]], the metric is called a [[metrički tenzor|metric tensor]]. |
|see_also=Cayley-Klein-Hilbert Metric, Distance, Equivalent Metrics, French Metro Metric, Fundamental Forms, Hedgehog Metric, Hyperbolic Metric, Metric Entropy, Metric Equivalence Problem, Metric Space, Metric Tensor, Metric Topology, Part Metric, Pseudometric, Riemannian Metric, Taxicab Metric, Ultrametric}} | |see_also=Cayley-Klein-Hilbert Metric, Distance, Equivalent Metrics, French Metro Metric, Fundamental Forms, Hedgehog Metric, Hyperbolic Metric, Metric Entropy, Metric Equivalence Problem, Metric Space, Metric Tensor, Metric Topology, Part Metric, Pseudometric, Riemannian Metric, Taxicab Metric, Ultrametric}} | ||
Trenutačna izmjena od 09:10, 20. listopada 2016.
Definicija: funkcija \( d\) na skupu \( X\) koja svakomu paru točaka \( (x,y)\) pridružuje nenegativni realni broj \( d(x,y)\) koji je nula ako i samo ako je \( x=y\) i koja zadovoljava simetriju \( d(x,y)=d(y,x)\) i nejednakost trokuta \(d(x,y)+d(y,z) \geqslant d(x,z)\)
Dopušteni nazivi: udaljenost, funkcija udaljenosti
Podređeni nazivi: euklidska metrika
Engleske istovrijednice: metric
Struna ID: 30165
Obrađivač: Zoran Škoda
Faza obrade: zaključaj naziv
Vrsta riječi: imenica Rod: ženski Broj: jednina
Cilj projekta "Hrvatsko nazivlje u matematici" je na jednom mjestu prikupiti i obraditi sve hrvatske nazive koji na izravan ili neizravan način imaju veze s matematikom. Ako želite na bilo koji način doprinijeti ostvarenju ciljeva ovog projekta, molim javite se voditelju projekta na adresu goran.igaly@math.hr
WMW naziv: metric
WMW klasifikacija: Calculus and Analysis > Differential Geometry > Metrics >
WMW definicija: A nonnegative function \( g(x,y)\) describing the "distance" between neighboring points for a given set. A metric satisfies the triangle inequality \(g(x,y)+g(y,z)>=g(x,z)\) (1) and is symmetric, so \(g(x,y)=g(y,x)\) (2)
A metric also satisfies \(g(x,x)=0\), (3) as well as the condition that \(g(x,y)=0\) implies \(x=y\).
WMW napomena: If this latter condition is dropped, then \( g(x,y)\) is called a pseudometric instead of a metric.
A set possessing a metric is called a metric space. When viewed as a tensor, the metric is called a metric tensor.
WMW See also: Cayley-Klein-Hilbert Metric, Distance, Equivalent Metrics, French Metro Metric, Fundamental Forms, Hedgehog Metric, Hyperbolic Metric, Metric Entropy, Metric Equivalence Problem, Metric Space, Metric Tensor, Metric Topology, Part Metric, Pseudometric, Riemannian Metric, Taxicab Metric, Ultrametric
Izvor: Weisstein, Eric W. "Metric." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Metric.html
Struna ID: 30165