The name of a mathematical property
0
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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
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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
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3
$begingroup$
I would call it "closure under multiplication".
answered Dec 18 '18 at 22:12
user247327user247327
11.6k1516
$endgroup$
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 |
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1 Answer
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1 Answer
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3
$begingroup$
I would call it "closure under multiplication".
answered Dec 18 '18 at 22:12
user247327user247327
11.6k1516
$endgroup$
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
11.6k1516
$endgroup$
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
11.6k1516
$endgroup$
I would call it "closure under multiplication".
answered Dec 18 '18 at 22:12
user247327user247327
11.6k1516
answered Dec 18 '18 at 22:12
user247327user247327
11.6k1516
answered Dec 18 '18 at 22:12
user247327user247327
11.6k1516
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
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 |
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$begingroup$
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