Was listening to strangs lecture on diagonalization  Well , let me ask you one thing ……. why to study it at all

Whats the point of knowing the decompostion of a matrix in to S D Sinv… Remember it always is S times D

BECOZ

the derivation goes like

AS = DS

where D is the diagnol matrix with eigen values on the diagonal  Ok, whats the big deal about diagnolization

WELL , once I can diagonalize, I can calulate the powers of A very easily….Eigen vectors dont change, but eigen values gets multiplied

Thats the  key..

Another brilliant fact is that : You can always solve a recurrence relation

For example, a fibonacci … you basically figure out a way to change the recurrence relation to a matrix equation

then you diagnolize it and you can then write the equation for a growing system

Thats a wonderful idea

This means that for an evolving system, the eigen values and eigen vectors of the first order difference equation is the key.

I am certain that hamilton would have dealt it that way

Let me check .

But this 20 min talk by strang in lecture 16 was too too superb..I somehow really am surprised at what all new things one can learn from revisiting profs lectures

I heard this lecture in the cab ride back to my home. I am blogging about it while in the cab.

Why ? Becoz …well, its a marathon..you got to run , irrespective of wherever you are..

Takeaway

  • Evolving System == Diagnolization
  • Diagonlization == eigen values and eigen vectors
  • Repeated eigen values means basically you are screwed as the matrix cannot be diagonlized
  • Det A – Lambda I = 0 gives the characteristic equation which will help you solve the equation

I CHECKED HAMILTON JUST NOW AND HE WAS USING EIGEN VECTORS AND Using DIAGNOLIZATION…. wow!!! I AM SUPER HAPPY  that I could immediately make the connection between strangs lecture and solving ARMA equations.  Strang’s words — Now you can solve dynamic evolving systems…actually helped me make the connection