Relationship between kernel function and basis
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2
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Is there any relationship between a kernel function and the concept of basis in a vector space?
For example does an equality like this
$$
g(x) = int_{Omega} alpha(y) K(x,y)dy
$$
have anything to do with something like
$$
g(x) = sum_{i}alpha_iK_i(x)
$$
?
Is there any concept of "uncountable" basis maybe?
linear-algebra functional-analysis soft-question
asked Nov 15 at 14:19
user8469759
1,2881516
add a comment |
up vote
2
down vote
favorite
Is there any relationship between a kernel function and the concept of basis in a vector space?
For example does an equality like this
$$
g(x) = int_{Omega} alpha(y) K(x,y)dy
$$
have anything to do with something like
$$
g(x) = sum_{i}alpha_iK_i(x)
$$
?
Is there any concept of "uncountable" basis maybe?
linear-algebra functional-analysis soft-question
asked Nov 15 at 14:19
user8469759
1,2881516
1
see here: en.wikipedia.org/wiki/Mercer%27s_theorem
– Hamed
Nov 15 at 15:07
Given it's a soft question, can't you just summarize few keypoints in an answer?
– user8469759
Nov 15 at 15:52
The thing is my knowledge of this area is pretty shallow. Even if it's a soft question, I don't wanna possibly write nonsense as an answer. Hopefully, someone more knowledgeable will come along and provide those key points.
– Hamed
Nov 15 at 18:58
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Is there any relationship between a kernel function and the concept of basis in a vector space?
For example does an equality like this
$$
g(x) = int_{Omega} alpha(y) K(x,y)dy
$$
have anything to do with something like
$$
g(x) = sum_{i}alpha_iK_i(x)
$$
?
Is there any concept of "uncountable" basis maybe?
linear-algebra functional-analysis soft-question
asked Nov 15 at 14:19
user8469759
1,2881516
Is there any relationship between a kernel function and the concept of basis in a vector space?
For example does an equality like this
$$
g(x) = int_{Omega} alpha(y) K(x,y)dy
$$
have anything to do with something like
$$
g(x) = sum_{i}alpha_iK_i(x)
$$
?
Is there any concept of "uncountable" basis maybe?
linear-algebra functional-analysis soft-question
linear-algebra functional-analysis soft-question
asked Nov 15 at 14:19
user8469759
1,2881516
asked Nov 15 at 14:19
user8469759
1,2881516
asked Nov 15 at 14:19
user8469759
1,2881516
asked Nov 15 at 14:19
user8469759
1,2881516
asked Nov 15 at 14:19
user8469759
1,2881516
1,2881516
1
see here: en.wikipedia.org/wiki/Mercer%27s_theorem
– Hamed
Nov 15 at 15:07
Given it's a soft question, can't you just summarize few keypoints in an answer?
– user8469759
Nov 15 at 15:52
The thing is my knowledge of this area is pretty shallow. Even if it's a soft question, I don't wanna possibly write nonsense as an answer. Hopefully, someone more knowledgeable will come along and provide those key points.
– Hamed
Nov 15 at 18:58
add a comment |
1
see here: en.wikipedia.org/wiki/Mercer%27s_theorem
– Hamed
Nov 15 at 15:07
Given it's a soft question, can't you just summarize few keypoints in an answer?
– user8469759
Nov 15 at 15:52
The thing is my knowledge of this area is pretty shallow. Even if it's a soft question, I don't wanna possibly write nonsense as an answer. Hopefully, someone more knowledgeable will come along and provide those key points.
– Hamed
Nov 15 at 18:58
1
1
see here: en.wikipedia.org/wiki/Mercer%27s_theorem
– Hamed
Nov 15 at 15:07
see here: en.wikipedia.org/wiki/Mercer%27s_theorem
– Hamed
Nov 15 at 15:07
Given it's a soft question, can't you just summarize few keypoints in an answer?
– user8469759
Nov 15 at 15:52
Given it's a soft question, can't you just summarize few keypoints in an answer?
– user8469759
Nov 15 at 15:52
The thing is my knowledge of this area is pretty shallow. Even if it's a soft question, I don't wanna possibly write nonsense as an answer. Hopefully, someone more knowledgeable will come along and provide those key points.
– Hamed
Nov 15 at 18:58
The thing is my knowledge of this area is pretty shallow. Even if it's a soft question, I don't wanna possibly write nonsense as an answer. Hopefully, someone more knowledgeable will come along and provide those key points.
– Hamed
Nov 15 at 18:58
add a comment |
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1
see here: en.wikipedia.org/wiki/Mercer%27s_theorem
– Hamed
Nov 15 at 15:07
Given it's a soft question, can't you just summarize few keypoints in an answer?
– user8469759
Nov 15 at 15:52
The thing is my knowledge of this area is pretty shallow. Even if it's a soft question, I don't wanna possibly write nonsense as an answer. Hopefully, someone more knowledgeable will come along and provide those key points.
– Hamed
Nov 15 at 18:58