So welcome back.
We have previously learned why this an eigenvalue problem, and it is not really a problem because we
can solve the eigenvalues of this matrix and these will be lambda and they are directly related to the
eigen frequencies.
And so we have to solve now this equation for its eigenvalues, and then we can analyze our numerical
solution for the item frequencies and can we can figure out if we can see the ion frequencies here in
the solution as well.
So what we have to do is we have to calculate the eigenvalues and we can of course, do this using an
umpire routine.
So first of all, we must, of course, to find the matrix.
So A is equal to NPL three, and then we can just straightforwardly write the numbers here to column
minus one comma zero.
And then the next line would be minus one to minus one and then zero minus one two.
And the number high routine is NPR dot org charts.
I think vowels and then the Matrix A. C. This is the solution.
These are the eigenvalues of this matrix.
So this is pretty easy, but I think it's now a pretty good time for you to exercise a bit programming
in Python.
Because what we have to do or what happens in this routine is that the routine solves this.
This equation here, it solves the equation, and zero is equal to the determinant of the matrix that
is given by a minus lambda times the identity matrix.
So now it's your turn.
You continue to write in this notebook and you try to define the function that, first of all, calculates
determinant.
Then you define another function which solves this equation here.
So basically, it calculates the routes the zeros after is determined here, which will be a polynomial
function.
And then it will give you the eigenvalues that we have found here by using this very simple routine.
So this is, of course, not really necessary.
And if you don't want to do it, if you don't have the time, it's no problem.
You can just skip over it or just watch my solution in the next lecture, because in the end, we will
always use this one.
But I think it's a good exercise and we will learn quite a lot in practice what we have learned before.