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Himanshu Raj
2007-Feb-08, 10:00 AM
What does Normalization in mathematics mean?

Sock puppet
2007-Feb-08, 10:53 AM
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.

clop
2007-Feb-08, 11:01 AM
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

Sock puppet
2007-Feb-08, 11:42 AM
Thanks clop, that was much better.

clop
2007-Feb-08, 11:57 AM
Aw thanks Sock_puppet, maybe my recent glass of Liffey water helped.

Sock puppet
2007-Feb-08, 12:20 PM
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....

clop
2007-Feb-08, 12:33 PM
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....

It's a euphemism for ness a guin. Surely you would know that.

satori
2007-Feb-08, 02:13 PM
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!)

Delvo
2007-Feb-08, 02:29 PM
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?

Blob
2007-Feb-08, 02:32 PM
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

Sock puppet
2007-Feb-09, 10:45 AM
It's a euphemism for ness a guin. Surely you would know that.

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.

Disinfo Agent
2007-Feb-09, 08:37 PM
What does Normalization in mathematics mean?"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.

satori
2007-Feb-11, 02:54 PM
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).

ToSeek
2007-Feb-11, 04:08 PM
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

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.

satori
2007-Feb-11, 05:38 PM
normalisation=/=renormalisation