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
edited Dec 18 '18 at 22:43
Will Fisher
4,05311132
asked Dec 18 '18 at 21:49
user120911user120911
231110
$endgroup$
add a comment |
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
edited Dec 18 '18 at 22:43
Will Fisher
4,05311132
asked Dec 18 '18 at 21:49
user120911user120911
231110
$endgroup$
$begingroup$
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
add a comment |
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
edited Dec 18 '18 at 22:43
Will Fisher
4,05311132
asked Dec 18 '18 at 21:49
user120911user120911
231110
$endgroup$
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
edited Dec 18 '18 at 22:43
Will Fisher
4,05311132
asked Dec 18 '18 at 21:49
user120911user120911
231110
edited Dec 18 '18 at 22:43
Will Fisher
4,05311132
asked Dec 18 '18 at 21:49
user120911user120911
231110
edited Dec 18 '18 at 22:43
Will Fisher
4,05311132
edited Dec 18 '18 at 22:43
Will Fisher
4,05311132
edited Dec 18 '18 at 22:43
Will Fisher
4,05311132
4,05311132
asked Dec 18 '18 at 21:49
user120911user120911
231110
asked Dec 18 '18 at 21:49
user120911user120911
231110
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
add a comment |
$begingroup$
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
add a comment |
1 Answer
1
active
oldest
votes
3
$begingroup$
I would call it "closure under multiplication".
answered Dec 18 '18 at 22:12
user247327user247327
11.4k1516
$endgroup$
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
add a comment |
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
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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".
answered Dec 18 '18 at 22:12
user247327user247327
11.4k1516
$endgroup$
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
add a comment |
3
$begingroup$
I would call it "closure under multiplication".
answered Dec 18 '18 at 22:12
user247327user247327
11.4k1516
$endgroup$
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
add a comment |
3
3
3
$begingroup$
I would call it "closure under multiplication".
answered Dec 18 '18 at 22:12
user247327user247327
11.4k1516
$endgroup$
I would call it "closure under multiplication".
answered Dec 18 '18 at 22:12
user247327user247327
11.4k1516
answered Dec 18 '18 at 22:12
user247327user247327
11.4k1516
answered Dec 18 '18 at 22:12
user247327user247327
11.4k1516
answered Dec 18 '18 at 22:12
user247327user247327
11.4k1516
11.4k1516
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
add a comment |
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
add a comment |
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
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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
$begingroup$
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