The name of a mathematical property












0












$begingroup$


When two Gaussian equations are multipled together, the outcome is another Gaussian distribution. Roger R. Labbe Jr., author of "Kalman and Bayesian Filters in Python" calls this property "rare" and points out that $sin(x) sin(y)$, for example, does not yield a $sin()$.



My question is simply, does that property have a name?






definition normal-distribution kalman-filter







share|cite|improve this question











$endgroup$












  • $begingroup$
    What do you mean "two Gaussian distributions are multiplied together"? Two Gaussian random variables or two Gaussian densities?
    $endgroup$
    – Henry
    Dec 18 '18 at 22:08










  • $begingroup$
    The exact quote is "The mathematics of the Kalman Flter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result"
    $endgroup$
    – user120911
    Dec 18 '18 at 22:15






  • 1




    $begingroup$
    What do you call "Gaussian equation" ?
    $endgroup$
    – Damien
    Dec 18 '18 at 22:34










  • $begingroup$
    The author shouldn’t have used the word “equation” — this is a terrible red flag. All the author is saying is that the product of two exponentials (and in particular Gaussians) is again an exponential. In other words, the class of exponential functions (those of the form $e^{f(t)}$) is closed under multiplication.
    $endgroup$
    – symplectomorphic
    Dec 18 '18 at 23:56
















0












$begingroup$


When two Gaussian equations are multipled together, the outcome is another Gaussian distribution. Roger R. Labbe Jr., author of "Kalman and Bayesian Filters in Python" calls this property "rare" and points out that $sin(x) sin(y)$, for example, does not yield a $sin()$.



My question is simply, does that property have a name?






definition normal-distribution kalman-filter







share|cite|improve this question











$endgroup$












  • $begingroup$
    What do you mean "two Gaussian distributions are multiplied together"? Two Gaussian random variables or two Gaussian densities?
    $endgroup$
    – Henry
    Dec 18 '18 at 22:08










  • $begingroup$
    The exact quote is "The mathematics of the Kalman Flter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result"
    $endgroup$
    – user120911
    Dec 18 '18 at 22:15






  • 1




    $begingroup$
    What do you call "Gaussian equation" ?
    $endgroup$
    – Damien
    Dec 18 '18 at 22:34










  • $begingroup$
    The author shouldn’t have used the word “equation” — this is a terrible red flag. All the author is saying is that the product of two exponentials (and in particular Gaussians) is again an exponential. In other words, the class of exponential functions (those of the form $e^{f(t)}$) is closed under multiplication.
    $endgroup$
    – symplectomorphic
    Dec 18 '18 at 23:56














0












0








0





$begingroup$


When two Gaussian equations are multipled together, the outcome is another Gaussian distribution. Roger R. Labbe Jr., author of "Kalman and Bayesian Filters in Python" calls this property "rare" and points out that $sin(x) sin(y)$, for example, does not yield a $sin()$.



My question is simply, does that property have a name?






definition normal-distribution kalman-filter







share|cite|improve this question











$endgroup$




When two Gaussian equations are multipled together, the outcome is another Gaussian distribution. Roger R. Labbe Jr., author of "Kalman and Bayesian Filters in Python" calls this property "rare" and points out that $sin(x) sin(y)$, for example, does not yield a $sin()$.



My question is simply, does that property have a name?






definition normal-distribution kalman-filter




definition normal-distribution kalman-filter






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 18 '18 at 22:43









Will Fisher

4,05311132




4,05311132










asked Dec 18 '18 at 21:49









user120911user120911

231110




231110












  • $begingroup$
    What do you mean "two Gaussian distributions are multiplied together"? Two Gaussian random variables or two Gaussian densities?
    $endgroup$
    – Henry
    Dec 18 '18 at 22:08










  • $begingroup$
    The exact quote is "The mathematics of the Kalman Flter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result"
    $endgroup$
    – user120911
    Dec 18 '18 at 22:15






  • 1




    $begingroup$
    What do you call "Gaussian equation" ?
    $endgroup$
    – Damien
    Dec 18 '18 at 22:34










  • $begingroup$
    The author shouldn’t have used the word “equation” — this is a terrible red flag. All the author is saying is that the product of two exponentials (and in particular Gaussians) is again an exponential. In other words, the class of exponential functions (those of the form $e^{f(t)}$) is closed under multiplication.
    $endgroup$
    – symplectomorphic
    Dec 18 '18 at 23:56


















  • $begingroup$
    What do you mean "two Gaussian distributions are multiplied together"? Two Gaussian random variables or two Gaussian densities?
    $endgroup$
    – Henry
    Dec 18 '18 at 22:08










  • $begingroup$
    The exact quote is "The mathematics of the Kalman Flter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result"
    $endgroup$
    – user120911
    Dec 18 '18 at 22:15






  • 1




    $begingroup$
    What do you call "Gaussian equation" ?
    $endgroup$
    – Damien
    Dec 18 '18 at 22:34










  • $begingroup$
    The author shouldn’t have used the word “equation” — this is a terrible red flag. All the author is saying is that the product of two exponentials (and in particular Gaussians) is again an exponential. In other words, the class of exponential functions (those of the form $e^{f(t)}$) is closed under multiplication.
    $endgroup$
    – symplectomorphic
    Dec 18 '18 at 23:56
















$begingroup$
What do you mean "two Gaussian distributions are multiplied together"? Two Gaussian random variables or two Gaussian densities?
$endgroup$
– Henry
Dec 18 '18 at 22:08




$begingroup$
What do you mean "two Gaussian distributions are multiplied together"? Two Gaussian random variables or two Gaussian densities?
$endgroup$
– Henry
Dec 18 '18 at 22:08












$begingroup$
The exact quote is "The mathematics of the Kalman Flter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result"
$endgroup$
– user120911
Dec 18 '18 at 22:15




$begingroup$
The exact quote is "The mathematics of the Kalman Flter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result"
$endgroup$
– user120911
Dec 18 '18 at 22:15




1




1




$begingroup$
What do you call "Gaussian equation" ?
$endgroup$
– Damien
Dec 18 '18 at 22:34




$begingroup$
What do you call "Gaussian equation" ?
$endgroup$
– Damien
Dec 18 '18 at 22:34












$begingroup$
The author shouldn’t have used the word “equation” — this is a terrible red flag. All the author is saying is that the product of two exponentials (and in particular Gaussians) is again an exponential. In other words, the class of exponential functions (those of the form $e^{f(t)}$) is closed under multiplication.
$endgroup$
– symplectomorphic
Dec 18 '18 at 23:56




$begingroup$
The author shouldn’t have used the word “equation” — this is a terrible red flag. All the author is saying is that the product of two exponentials (and in particular Gaussians) is again an exponential. In other words, the class of exponential functions (those of the form $e^{f(t)}$) is closed under multiplication.
$endgroup$
– symplectomorphic
Dec 18 '18 at 23:56










1 Answer
1






active

oldest

votes


















3












$begingroup$

I would call it "closure under multiplication".






share|cite|improve this answer









$endgroup$









  • 1




    $begingroup$
    This is a comment, IMO.
    $endgroup$
    – coffeemath
    Dec 18 '18 at 22:17










  • $begingroup$
    @coffeemath while the answer is short, it is an answer. It is incomplete, though. Give evidence that this is standard nomenclature. For instance: "groups are closed under multiplication as a definition" cite that sort of language in literature.
    $endgroup$
    – Larry B.
    Dec 18 '18 at 23:21










  • $begingroup$
    user247327-- Re-reading OP's post I agree it asked only for a name of the property. I can delete comment if you want.
    $endgroup$
    – coffeemath
    Dec 19 '18 at 5:36












Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3045753%2fthe-name-of-a-mathematical-property%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









3












$begingroup$

I would call it "closure under multiplication".






share|cite|improve this answer









$endgroup$









  • 1




    $begingroup$
    This is a comment, IMO.
    $endgroup$
    – coffeemath
    Dec 18 '18 at 22:17










  • $begingroup$
    @coffeemath while the answer is short, it is an answer. It is incomplete, though. Give evidence that this is standard nomenclature. For instance: "groups are closed under multiplication as a definition" cite that sort of language in literature.
    $endgroup$
    – Larry B.
    Dec 18 '18 at 23:21










  • $begingroup$
    user247327-- Re-reading OP's post I agree it asked only for a name of the property. I can delete comment if you want.
    $endgroup$
    – coffeemath
    Dec 19 '18 at 5:36
















3












$begingroup$

I would call it "closure under multiplication".






share|cite|improve this answer









$endgroup$









  • 1




    $begingroup$
    This is a comment, IMO.
    $endgroup$
    – coffeemath
    Dec 18 '18 at 22:17










  • $begingroup$
    @coffeemath while the answer is short, it is an answer. It is incomplete, though. Give evidence that this is standard nomenclature. For instance: "groups are closed under multiplication as a definition" cite that sort of language in literature.
    $endgroup$
    – Larry B.
    Dec 18 '18 at 23:21










  • $begingroup$
    user247327-- Re-reading OP's post I agree it asked only for a name of the property. I can delete comment if you want.
    $endgroup$
    – coffeemath
    Dec 19 '18 at 5:36














3












3








3





$begingroup$

I would call it "closure under multiplication".






share|cite|improve this answer









$endgroup$



I would call it "closure under multiplication".







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 18 '18 at 22:12









user247327user247327

11.6k1516




11.6k1516








  • 1




    $begingroup$
    This is a comment, IMO.
    $endgroup$
    – coffeemath
    Dec 18 '18 at 22:17










  • $begingroup$
    @coffeemath while the answer is short, it is an answer. It is incomplete, though. Give evidence that this is standard nomenclature. For instance: "groups are closed under multiplication as a definition" cite that sort of language in literature.
    $endgroup$
    – Larry B.
    Dec 18 '18 at 23:21










  • $begingroup$
    user247327-- Re-reading OP's post I agree it asked only for a name of the property. I can delete comment if you want.
    $endgroup$
    – coffeemath
    Dec 19 '18 at 5:36














  • 1




    $begingroup$
    This is a comment, IMO.
    $endgroup$
    – coffeemath
    Dec 18 '18 at 22:17










  • $begingroup$
    @coffeemath while the answer is short, it is an answer. It is incomplete, though. Give evidence that this is standard nomenclature. For instance: "groups are closed under multiplication as a definition" cite that sort of language in literature.
    $endgroup$
    – Larry B.
    Dec 18 '18 at 23:21










  • $begingroup$
    user247327-- Re-reading OP's post I agree it asked only for a name of the property. I can delete comment if you want.
    $endgroup$
    – coffeemath
    Dec 19 '18 at 5:36








1




1




$begingroup$
This is a comment, IMO.
$endgroup$
– coffeemath
Dec 18 '18 at 22:17




$begingroup$
This is a comment, IMO.
$endgroup$
– coffeemath
Dec 18 '18 at 22:17












$begingroup$
@coffeemath while the answer is short, it is an answer. It is incomplete, though. Give evidence that this is standard nomenclature. For instance: "groups are closed under multiplication as a definition" cite that sort of language in literature.
$endgroup$
– Larry B.
Dec 18 '18 at 23:21




$begingroup$
@coffeemath while the answer is short, it is an answer. It is incomplete, though. Give evidence that this is standard nomenclature. For instance: "groups are closed under multiplication as a definition" cite that sort of language in literature.
$endgroup$
– Larry B.
Dec 18 '18 at 23:21












$begingroup$
user247327-- Re-reading OP's post I agree it asked only for a name of the property. I can delete comment if you want.
$endgroup$
– coffeemath
Dec 19 '18 at 5:36




$begingroup$
user247327-- Re-reading OP's post I agree it asked only for a name of the property. I can delete comment if you want.
$endgroup$
– coffeemath
Dec 19 '18 at 5:36


















draft saved

draft discarded




















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid …



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3045753%2fthe-name-of-a-mathematical-property%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







-

Popular posts from this blog

Plaza Victoria

Image
Plaza Victoria Plaza Victoria en 2017 Otros nombres Plaza de La Victoria Localización El Almendral, Valparaíso, Chile Vías adyacentes Chacabuco, Molina, Plaza Victoria y Edwards Creación 1841 Metro Bellavista Ubicación 33°02′46″S 71°37′11″O  /  -33.04624167, -71.61980833 Coordenadas: 33°02′46″S 71°37′11″O  /  -33.04624167, -71.61980833 [editar datos en Wikidata] La Plaza Victoria , también llamada Plaza de la Victoria , [ 1 ] ​ es una plaza ubicada en el sector El Almendral del plan de la ciudad de Valparaíso, Chile, de importancia patrimonial, que incluye valiosas estatuas y especies vegetales. [ 2 ] ​ La plaza se creó como tal en la primera mitad del siglo XIX, tomando previamente los nombres de Plaza Nueva y Plaza de Orrego . Si bien desde sus inicios tuvo relevancia histórica, no fue sino a partir de fines de los años 1860 cuando comenzó a cobrar mayor importancia y se convirtió en uno de los principales centros sociales de l...
Read more

Puebla de Zaragoza

Image
Para otros usos de este término, véase Puebla (desambiguación). Heroica Puebla de Zaragoza Localidad De arriba a abajo de izquierda a derecha: Estrella de Puebla, Volcán Popocatépetl, Catedral de Puebla, Monumento a Ignacio Zaragoza, Estadio Cuauhtémoc, Angelópolis y Vista panorámica de la ciudad. Escudo Otros nombres: El relicario de América/ La ciudad de los Ángeles/ La Angelópolis Lema: Muy noble y muy leal ciudad de Puebla de los Ángeles Heroica Puebla de Zaragoza Localización de Heroica Puebla de Zaragoza en México Heroica Puebla de Zaragoza Localización de Heroica Puebla de Zaragoza en Puebla Mapa interactivo Coordenadas 19°03′05″N 98°13′04″O  /  19.051388888889, -98.217777777778 Coordenadas: 19°03′05″N 98°13′04″O  /  19.051388888889, -98.217777777778 Idioma oficial Español Entidad Localidad  • País   México  • Estado Puebla  • Municipio Puebla Presidente municipal Claudia Rivera Vivanc...
Read more

Musa

Image
Para el género de plantas, véase Musa (planta). Apolo y la Nueve Musas En la mitología griega, las musas (en griego antiguo μοῦσαι « mousai» ) son, según los escritores más antiguos, las divinidades inspiradoras de las Artes: cada una de ellas está relacionada con ramas artísticas y del conocimiento. Son hijas de Zeus y de Mnemósine, compañeras del séquito de Apolo, dios olímpico de la música y patrón de las bellas artes, quien tuvo romances con cada una de ellas, dejando descendientes. Bajaban a la tierra a susurrar ideas e inspirar a aquellos mortales que las invocaran. En la época más arcaica eran las ninfas inspiradoras de las fuentes, en las cuales eran adoradas. Finalmente, alrededor de los siglos VIII-VII a. C. [ 1 ] ​ prevaleció en todo el territorio de la Hélade la adoración de las nueve Musas, que son Calíope, Clío, Erato, Euterpe, Melpómene, Polimnia, Talía, Terpsícore y Urania. El culto a las musas era originalmente de Tracia y Beocia, y fueron de vital impo...
Read more