Positively Definite Gilmas

Hello Fellow Gilmas,

Though all of us know that we are Gilmas by birth, we find it sometime difficult to characterize a randomly sampled human being as a gilma or non-gilma. This is of course a binary classification problem that involves a parameter Gil that we need to estimate.

But before going too far into gilmaness and the classification problem, let us try to understand some fundamental facts about gilma.

As we all have observed in ourselves and among fellow gilmas, the following two things hold true always

Observation 1: When two gilmas meet, they invariably talk about 'gilmaism' !
Observation 2: However constant pressure you apply to a gilma, he will never become a non-gilma (and hence will stay as a gilma).


Surprise Surprise!!!

These are fundamental statements that we have made to define something called as 'Gilma Space' !!


Gilma Space
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Formally, we have the following


Given a Gilma Space Gil , if g1,g2 are two gilmas belonging to Gil, then
g1 + g2 is also gilma (Direct from Observation 1).

Given a Gilma Space Gil, if g1 is a gilma , then any 'constant' pressure applied to this gilma will again result in a gilma

i.e c * g1 also belongs to Gil.



Thus we can arrive at the following conclusion.

"Any linear combination of Gilmas is again a Gilma" (Gheorem 1)
(This result was established by Gilmananda in the celeberated paper 'On Jipis, Japoosis and Gilmas - A rigorous formulation of gilmaism' )


Zero Gilmas
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Whenever a Gilma is born in this world, he has no knowledge of anything or anybody. Yet he is a gilma. Such Gilma's are called Zero Gilmas.


Positive Definite Gilmas
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This is the killer!!

This is a hugely successful test to figure out if a random guy/girl is positively and definitely a gilma or not.

Before defining it formally, let us look at the intuition.

Assume a non-gilma (note again, non-gilma) is suddenly left inbetween a group of gilmas. It is bleeding obvious that the non-gilma will be irritated like anything until he/she becomes totally down. Sometimes the non-gilma will develop a lot of negative feelings that he/she might try to jump like a monkey. (Such scenarios are commonly found to occur in non-gilmas with more than one girl/boy friends though no rigorous proof is arrived yet. In other words, it is a open gilma problem! )

Converting the above intuition into mathematics, we have the formulation as gelow..i mean..below.

Let us consider a set of n^2 gilmas. Let us name them as G(i,j) where i , j range from 1 to n. Now if we define a n*n matrix M such that each gilma G(i,j) goes and sits in position (i,j) and starts to irritate a non-gilma Z, then Z develops negative feelings and so

Z(t) * M * Z < 0 (negative)
[ Here Z(t) indicates transpose of Z i.e non-gilma Z tries to sit in a different pose but still fails]


Whereas if we allow a gilma to be Z, then we are sure that gilma Z will NOT be irritated by the conversation. On the contrary his gilma co-efficient will grow tremendously that he will be filled with positive energy.

In Mathematical terms,

Z(t) * M * Z > 0 (positive).


Thus if the value of Z(t) * M * Z is positive, then we have a definite gilma!!

This is the 'Positive Definite Gilma' test.

This had proved tremondously successful in many undergraduate colleges. We request fellow gilmas to try it out and let us know the results.

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Caveat:

We have left out the case when Z(t) * M * Z is 0 because the author currently has no sufficiently silly explanation for it !

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