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According to this question, the etymology of the terms is related, and Kernel is used to mean the "core" of something. In general it seems to refer to an unchanging transformation at the heart of a maths problem

In linear algebra, a Kernel is the vector space for which a matrix always go to zero.

In statistics, I have seen the term "kernel X" used to describe various types of weighting function.

Wikipedia indicates that, in statistical analysis, it's considered a window function.

In the case of Linear Algebra, the Kernel vector space could be considered a matrix transformation. Does the same apply to the Kernel in Statistics? Can the weighting function, or window function be considered a transformation?

kjetil b halvorsen
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Connor
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    FYI: “kernel” has at least two meanings in statistics https://stats.stackexchange.com/a/2500/35989 If you look at Wkipiedia, the word is used in many contexts https://en.wikipedia.org/wiki/Kernel Words are ambiguous. – Tim Feb 09 '23 at 21:57
  • True, but mathematics is so precise in so many ways that it's strange when the words don't follow suit! I take it your comment means that it is a coincidence? – Connor Feb 09 '23 at 22:12
  • That's why mathematics has its own (mathematical) language rather than relying on English (or whatever) language. – Tim Feb 10 '23 at 07:39
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    I you can't find at least 10 distinct meanings for "kernel" in mathematics, you're not searching hard enough;-). – whuber Feb 10 '23 at 15:01
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    the general answer to these questions must be YES, as probability theory is almost an application of functional analysis which includes linear algebra. any concept in statistics has some representation in linear algebra. the nuance is that you may name something in stats while its representation in linear algebra may have a different name. in case of Kernel at least in some contexts the term refers to mirroring concepts in stats and linear algebra. moreover Kernel also refers to a similar concept in machine learning domain too, see e.g. "kernel trick" in SVM – Aksakal Feb 10 '23 at 16:34
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    @Aksakal The extreme reduction of statistics to linear algebra suggested in that comment flies in the face of much of the statistical literature, especially any part of it concerned with modeling nonlinear phenomena. It also neglects the important fact that statistics is not mathematics: the math is used to help us understand and develop the statistical concepts but it is not the same thing. – whuber Feb 11 '23 at 13:03
  • @whuber, that's why I wrote functional analysis to cover everything, though a lot of stats mirrors linear algebra. I agree though that theory of probabilities is not a simple application of math, thus almost qualifier in my comment – Aksakal Feb 11 '23 at 23:06
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    @Aksakal I suppose you could roll up most of mathematics under the functional analysis flag -- at which point calling something an application of functional analysis isn't telling us anything. – whuber Feb 12 '23 at 15:04

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