Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -




Not registered yet?

Post a reply

Go back

Write your message and submit
:) :| :( :D :o ;) :/ :P :lol: :mad: :rolleyes: :cool: | :dizzy :eek :kiss :roflol :rolleyes :shame :down :up :touched :sleep :wave :swear :tongue :what :faint :dunno

Go back

Topic review (newest first)

2013-01-26 10:38:41


Before going on with a new idea I suggest a look at "Matrix Moves" in this thread.

Supposing we have the stochastic matrix

The central problems of Linear Algebra are the solution of a simultaneous set of linear equations or Ax = b and determining the eigenvalues of a matrix.

The eigenvalues are usually computed using a computer and we will not break with tradition, they are

There is a little theorem that says if a square matrix has distinct eigenvalues then it is diagonalizable. So this one is diagonalizable.

To do it we need the Eigenvectors of A:

To check whether we have diagonalized it we plug in to

Okay, so what? The useful fact is that to get A^k we only now need the following matrix equation.

Now D^k is easy to get because to raise a matrix with just diagonal elements like D to the kth power you just take each element and raise it to the kth power.

So if we wanted A^10 we would compute

And we are done!

Board footer

Powered by FluxBB