What is Eigenvectors: Definition and 458 Discussions
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by
λ
{\displaystyle \lambda }
, is the factor by which the eigenvector is scaled.
Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated.
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...