@Carl Love 

The 2x2 identity matrix and the 2x2 zero matrix are both non-defective.
You should consider e.g. [[0,0],[0,0]] and [[0,1],[0,0]].

Edit: We may say that among the matrices with a single eigenvalue, the "majority" are defective.

I have included both stats.

@Christopher2222 

EurosimGrxxxkn1.mw

@Christopher2222 

This was really easy.
The delicate problem is to find a solid generator for scores X versus Y, knowing the rankings x and y.
I am not a statistician, but probably such problems are treated somewhere.

EurosimGrxxxkn.mw

@Christopher2222 

I have uploaded a corrected version.

Here is a simulation including qualifications from groups.
The qualification part is a bit un-orthodox because the points are chosen randomly around 1 and 3.
Maybe this should be fine-tuned -- the procedure myscor(i,j) -- using a nonuniform distribution
["Continuous" points have the advantage of avoiding the ties]

Also instead of using the "17.03" table to determines the third place matches,
a simple search was used, but respecting the "17.02" directive.

EurosimGrxxx.mw

edit: corrected

@Christopher2222 

The code does not update the ELOs. It is not difficult to include this.

It is also easy to include the group rounds (at least without graphics, unless it's done by someone knowing Maplets), but I do not know exaclty the qualification algorithm. AFAIK the first 2 teams in each group are automatically qualified.

In order to have a more realistic simulation one must decide when a draw occurs; probably something like outcome(X_versus_Y) in [0.5-e,0.5+e] for some e>0, e.g. e=0.1 or 0.2.

@Carl Love 

Of course, thank you.

@Mariusz Iwaniuk 

Try

plots[odeplot](de, [x, diff(y(x),x,x)^2 - 1], x=0..1);

OK,  so, if rating(X)=x, rating(Y)=y  ==>

Prob(X_beats_Y) = 1 / (1 + 10^((y-x)/400))

@Christopher2222 

Do you know how the ELO ratings are computed?
If two teams X,Y have the ratings x,y what is the probability for X to win?

(I see in the worksheet that Gumbel distribution is used, but I wonder why it was chosen.)

@Lola 

Your function mi() is discontinuous in (tau,T) due to charfcn.This will creat problems for NLP. Also, charfcn is probably not the best choice for numerics.
I would recommend to investigate theoretically the problem.

For vizualization I suggest also e.g.:

Explore(plot(mi(10, 1, 5, 2, 2, 6, T, tau, 0.2, 0.2, 0.5),T=0..20,view=-1..1),tau=0.0..20.0,animate);

@Markiyan Hirnyk 

I don't know of course which summation method was used. But you can easily verify whether the result agrees with the one given by Euler's summation method.

@Zeineb 

That's simply because your new series is divergent.
Try e.g.

add(evalf(g(n)/n!),n=0..500);

@Markiyan Hirnyk 

What is aside? The Fibonacci sequence is a linear combination of geometric sequences, isn't it? Have you asked something else?

The geometric series Sum(z^n,n=0..infinity) converges to 1/(1-z) in Euler's sense,

see https://en.wikipedia.org/wiki/Euler_summation

@Markiyan Hirnyk