It has been so long since I have taken, or even used, most of the math in your videos, but I watch them every time you post one. Thank you for giving me exercises to keep my brain in shape!
i need some help, for lamda=2 i got [1 2 0] all of x are in term of x1, my ans isnt same as sir, if lamda=2 , in term of x2 i will get[ 2 1 0] which will be same as sir. does that mean for every diff Vector i can choose diff x to be in term of? or for example i choose x1,x2,x3 to be in term of x1 for lamda=1, lamda=2and lamda=3, all x have to in term of x1, sir did mention at the end of the video but just wanna double confirm which is the right one or i calculate wrongly, not sure
Does it matter which order we put the eigenvalues? For example if we did λ1 = 3, λ2 =2 , λ3 =1? I know how to answer this but my lecturer always has a different order of eigen values, which also changes the order of the eigen vectors
Did you figure out if the order matters or not, I'm also stuck on the same issue. Cause if we change the order of eigenvalues, i think we get different eigenvectors as well
How could it be like that? When we make the first determinant of lambda 2, X3 = 0, then we put 2(X2) instead of X1, and how come the vector [2 1 0] is obtained when lambda = 2? I don't understand, is there anyone who can explain it to me?
A (matrix) * [2 1 0] (Eigvector lambda2) = [4 2 0] = 2 (Eigval lambda2) * [2 1 0] A (matrix) * [1 2 1] (Eigvector lambda3) = [3 6 3] = 3 (Eigval lambda3) * [1 2 1] A is a matrix (an operator) that works on a vector to become a VALUE times that vector. That's the way to do a measurement in quantum mechanics.