Problem with spin interprestation related to matrics

1. Feb 4, 2008

Cyrus_101

context: teacher introduced sigma matrics, which have eigenvectors "a", to calculate the proability the spin switching state from "b" to "a" P=<a|b><a|b>conjugate

qustion: |b>= (1
0) ===>a vector, old state

and the sigma matric for example can be (0 1
1 0)===> which the eigenvector would be "a"
then the teacher said P=<a|b><a|b>conjugate will meature the proability the spin going from "y" axis to "x" axis. Matric are operators in linear transformation, My perception of matrics is that it does transform things in real space...but it does not indicate cordinate information...how come that the matrics indicate the spin state will switch to "x" axix in real space? appreciate for help!