Eigenvectors Definition and 462 Threads

The eigenvalues of the matrix \left(\begin{array}{cc}0 & \frac{1}{2}\\ \frac{1}{2} & 0\end{array}\right) are \lambda_1 = \frac{1}{2} and \lambda_2 = -\frac{1}{2} The problem here is that I have no idea of how to calculate the eigenvectors. Could some one please explain me, in detail, how...

Hi. Marix A= |1 1 0 | |0 2 0 | |2 1-1 | Has three eigenvectors [1,1,1]^T, [1,0,1]^T and [0,0,1]^T, By using this knowledge solve A^11. Ok, solving A^11 is rather easy with any decent calculator, or even with pen , paper and some time, but how on Earth I'm supposed to benefit...

this is no doubt older than dirt, but it just popped into my head when trying to think of how to convince my beginning linear algebra class that every linear isometry of R^3 has an eigenvector: i.e. it follows from the theorem that one cannot comb the hair on a billiard ball. do you see how...

I have a homework problem here I am a little at a loss on due to not very good examples in class and the part of the book that explains them is 4 chapters ahead and loaded with words I just do not understand yet. :bugeye: If someone could give a definition or two and get me started on this bad...

Can anyone give me some hints? I need to prove that all spinors to a spin-1/2 particle are eigenvectors to \hat S^2! /Daniel

Ok, so let us suppose we have a spinor which is a spin 1/2 state vector (a) (b) Now spinors exist in 2 dimensional complex space. How do I find the eigenvalues which correspond to the above...

Ok, so let us suppose we have a spinor which is a spin 1/2 state vector (a) b Now spinors exist in 2 dimensional complex space. How do I find the eigenvalues which correspond to the eigenvector (a) b I am confused because we are dealing...

The maximum # of mutually orthonormal eigenvectors of a Hermitian operator must be equal to 2*(number of coordinate basis vectors), where the 2 is for say spin 1/2. Now when solving the eigenvalue problem for the Hamiltonian operator, one of the boundary conditions is that the vector obtained...

spanning sets, eigenvalues, eigenvectors etc... can anyone please explain to me what a spanning set is? I've been having some difficulty with this for a long time and my final exam is almost here. also, what are eigenvalues and eigenvectors? i know how to calculate them but i don't understand...

I'm currently taking linear algebra and it has to be the worst math class EVER. It is extremely easy, but I find the lack of application discouraging. I really want to understand how the concepts arose and not simple memorize an algorithm to solve mindless operations, which are tedious. My...

Hi, I encountered the following HW problem which really confuses me. Could anyone please explain it to me? Thank you so much! The result of applying a Hermitian operator B to a normalized vector |1> is generally of the form: B|1> = b|1> + c|2> where b and c are numerical...

What's the utility of the eigenvectors of a matrix? I know that is something about quantum mechanics