- #1
quietrain
- 655
- 2
Homework Statement
i have matrix A which is diagonalisable
by doing an example on wiki under the section " how do diagonalise a matrix"
http://en.wikipedia.org/wiki/Diagonalizable_matrix
i realize that
A x is not equal to [itex]\lambda[/itex] x , where x are eigen vectors of A , [itex]\lambda[/itex] is eigen values
instead
x A = [itex]\lambda[/itex] x
and i think
A x = x [itex]\lambda[/itex]
QUESTION 1)
if this is so, why do they always write the hamiltonian as H |x> = E |x> ? shouldn't it be H |x> = |x> E ?
if i remembered correctly, for matrix multiplication AB =/= BA right?
but i read wiki and it says something like (i can't remember the exact phrasing)
"it is equal if both A and B are diagonalisable matrix , and are both n by n matrix. "
QUESTION 2)
also, for PT A P = [itex]\lambda[/itex]
if i want to "bring over" the P, is it like this
A = P [itex]\lambda[/itex] PT
but why is it like this?
thanks!