Could someone explain to me why it is that no matter what research project I undertake in no matter which subject, sooner or later I will find that my result ultimately hinges upon calculating the determinant of some truly hideous monster of a matrix?
Seriously: I study epidemiology, and it’s a monster-determinant. I study the area spectrum of quantum-corrected black holes: monster-determinant. I study the quasinormal mode spectrum of an acoustic dumb hole. I cudgel my brains out for months looking for a method–any method–that will work.
And what do I find when my long labours are done?
The algorithm to find these frequencies for a given ‘l’ is simple…(i) choose an N, (ii) define a function returning the determinant of the system, (iii) find the roots of interest…(iv) increase N until those roots become constant to the desired precision.
In other words: monster-determinants.
I don’t even know, honestly, why I bother looking for solutions to problems: especially problems that I’m looking to solve at the very end of my research. It’s always going to involve calculating the determinant of some matrix.