What does Normalization in mathematics mean?
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What does Normalization in mathematics mean?
What does Normalization in mathematics mean?
Established Member
It means setting the integral of a function equal to the known value, usually 1.
For example, if you were to take a QM wavefunction (giving you the probability of finding a certain particle in a given place), and integrate it over all the space the particle could be in, you know the probability of finding it is 1, because it has to be somewhere. So you set the integral equal to one, then look at what that tells you about previously unknown constants in your wavefunction.
Sorry if this is unclear, hopefully someone else will do a better job of explaining it.
Established Member
That seems like a rather specific description of normalisation.
The way I understand it, normalisation means scaling groups of data so that either the minimum and maximum values of each group are 0 and 1 respectively, or so that the area under a distribution curve of each group is equal to 1. This allows for valid comparison between the groups of data.
clop
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Thanks clop, that was much better.
Established Member
Aw thanks Sock_puppet, maybe my recent glass of Liffey water helped.
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Ack! You didn't drink Liffey water, did you? Ptoi! As in, the Liffey which flows through Dublin? I really hope it was from a loooong way upstream....
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It's a euphemism for ness a guin. Surely you would know that.Originally Posted by Sock puppet
Banned
A norm is a real valued function on a (any) vector space, sending o and only o to o, being otherwise strictly positive and obeing the triangular inequality F(a+b) smaler or equal F(a) +F(b). (basic!)
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The answers so far have described the process, but what about the results? What do you get from it? Why do you do it?
The first time I ran across the term, my guess about its meaning was that it reassigned values from a given real distribution such that the new values fit into a normal distribution instead of the original one... so if the original is skewed low then the process of normalization would shift some of the numbers upward, for example. (It was associated with a poll asking for numerical responses within a defined range, and seemed to be intended to move the "average" response to the middle of the given range.) Is that what normalization is about?
Order of Kilopi
Hum,
in physics its a great tool, or cheat, to get rid of infinities in equations and give meaningful results.
(infinity +3) x (infinity +3) = infinity --> renormalised = 9
http://en.wikipedia.org/wiki/Normalization
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Believe it or not, I've never heard it called that before. It's like with a lot of phrases like that: everyone know what it means except the people who are supposed to use it.
Order of Kilopi
"Normalization" has many different meanings in mathematics. You need to be more specific. The general idea, though, is to pick a particular element of a class (of functions, vectors, random variables), and reduce it to the "simplest" element in the class, so that you only need to deal with that simpler representative.
Banned
my previous post ( giving the definition for a vector space norm) was silly!
I am happy DisinfoAgent has finaly come up with the right answer ( I wanted to hand in myself now).
Vulcan Administrator
And it's an essential part of quantum physics, many of whose equations result in infinities without renormalization - oddly, not all equations permit renormalization, but somehow the particles only participate in the behavior modeled by equations that do (or so I have read). Very strange.
Everything I need to know I learned through Googling.
Banned
normalisation=/=renormalisation
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