## Saturday, October 25, 2008

### egan vectors and nayanthara transformations !

The purpose of a blog like this is to introduce mathematics that the author does not understand to the widespread readers who don't exist. The basic assumption here is that the non-existent reader understands the language tamizh. (not necessarily to the extent of thirukural or silapadhigaaram though familiarity of these advanced topics is considered a plus)

Ok.

Its diwali time and when better can we get started?!

Egan:
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If you haven't heard the term egan before, then you invariably fall into one of these three categories

-> You are not a tamilian !
-> You are a die hard vijay fan !
-> You watched 'billa 2007' till interval and then decided that it is a sin to spend money on movies anymore.

As most people in Tamilnadu fall into one of these three categories, i need to take a minute to explain what "Egan" is. But before that let me make one leap of faith assumption that you know who USA is. If you are saying to yourself that i should
have written 'What USA is' and not 'Who USA is', then you are Dismissed ! Doomed ! Busted! Whatever!
How on earth can a Tamilian think of the United States of America as the expansion for USA when there is a better and fitting expansion right here in Tamilnadu. Yes! It is none other than our own "Ultimate Star Ajithkumar".

Ok.
Lets move on !

If you do a Google Image search for Egan, the first picture that pops up is that of a girl in a mini skirt. But that's certainly not our "current" topic of interest (Yes! Neither the girl (Kian Egan), nor her mini skirt (Brown color)).
So lets forget the girl and define what Egan is.

Well..Well.. it is complicated !

And that's where Mathevettica comes to the rescue.

Here we go!

Egan to Eigen
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Well, if you happen to think both these terms sound pretty similar and so there could not be much of a difference in their semantics, then you got it right !

Eigen in some language (Italian probably) means 'characteristic' . Now Think of our USA and think of the word 'Characteristic'. Which word relates them together? Did you guess 'Failure?' . You are on the right track.

Eigen Vector
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Now onto some serious mathematics. Eigen Vector is the 'characteristic' vector of a "transformation". Wait a minute! What do i mean by a transformation? A transformation is nothing but a 'change'. You have a piece of wood in front of you and you tilt it a little bit, and that's a "transformation" of the wood for you !
If you represented each point on the wood by co-ordinates (x,y,z) and you tilt it, most of the points would now have gone to a different point in space (say x2,y2,z2 for each (x1,y1,z1)).
But note the use of the word "most". That means there might be some points that might not have changed its position at all!! Now i can hear you say 'hey..that's very specific to the transformation. It depends on how you tilt the piece of wood'. And i can't agree more. It is very specific to the transformation . In other words, it is 'characteristic' of the transformation. And such points (vectors) are exactly called the eigen vectors. They are characteristic of a transformation. They just don't change in direction! But wait a minute. The Eigen vectors will not change in direction. But then they can change in their magnitude. Think of a rubber band. Now if you pull the rubber band with full force with both hands, you are transforming its shape. But in the direction of your pull, the points just are transforming a little further in the same direction. (further here means distance/magnitude from the center).

Oh my goodness!

What on earth has all this crap got to do with USA?

Well, that's the crux of the post.

If you understood Eigen vectors already, then you can understand what 'Egan' is. Or if you already know what Egan is, try to get a hang of what Eigen vector . In either case, lets define the analogy below.

Analogy
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USA has decided to star in one more movie. Now don't start running towards the wall to bang your head. We all know it is unfortunate to the human community as a whole and we have to sail through sad times together. So lets make the best use of Egan by trying to understand the analogy with Eigen vectors.

What is the 'Characteristic' of an USA movie? 'Failure' - i can hear the shout from you guys! Now what if i say our beloved USA acts in two roles 'transforming' himself now and then. 'Failure still' !! Again, right answer folks. Now to one more question. It seems the director of this movie is Rajusundaram. What can you now say about this movie? Excellent going guys, it is the same answer and it fits very well everywhere!

"Failure" !

To summarize
No matter what happens i.e no matter how USA transforms himself in his movies, the direction will still be the same - crap!! So that's the closest you can get to Eigen vectors!

One final word:
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I have a question for you folks. Before that let me quickly explain the term 'Eigen value' in one sentence.

'Eigen value' is the amount by which a Eigen vector changes in magnitude after a transformation. (of course, there is no change in direction)

Now what could be a possible, plausible "Egan value" of the movie???

In other words, if at all someone goes and watches this movie, what could be the value?

Guess why? :)

Of course. You got it right again... the only "Egan Value" is Nayanthara !!!

There you go!!! That brings us to the end.
Good bye and happy Diwali till we meet for the next stupid tutorial !

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If in the most unfortunate case you wanted to seriously kick the author's
butt, here is the contact address.

Arun R,
Department of CSA,
Indian Institute of Science,
Bangalore.

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Girish said...

lol.. funny!! nice work..

C.Charanya said...

Super!!! Eigen vectors tension ayidum!!!Athu epdi u r able to hear the reader's responses???

s()ms!e said...

I thought u had a way with words.. looks like u have a way with numbers too :) Liked the analogy and the nayanthara part(Eigen value)!

P.S. - Pls update the Gilmananda blog!