The discussion revolves around finding eigenvectors for two matrices, V and T, given their eigenvalues. Participants are exploring the methodology for determining eigenvectors and clarifying the implications of their calculations.
The conversation is active, with participants providing feedback on each other's understanding and methods. Some guidance has been offered regarding the nature of eigenvectors and their normalization, though no consensus has been reached on specific steps or methods.
Participants are navigating potential confusion regarding the setup of the problem, particularly with the matrices involved and the interpretation of eigenvalues. There is also mention of normalization and the representation of eigenvectors, indicating a focus on the properties of these mathematical entities.
abszero said:Eigenvectors are determined up to a multiplicative constant, so [1 -1] is the same eigenvector as [-1 1] as far as the eigenvalue goes. Now, if they form a degenerate subspace (i.e. they both have eigenvalue 2) things get slightly more interesting, but not really.
We can say this more precisely: either of these eigenvectors constitute a basis for the eigenspace associated with this eigenvalue.Eigenvectors are determined up to a multiplicative constant, so [1 -1] is the same eigenvector as [-1 1] as far as the eigenvalue goes. Now, if they form a degenerate subspace (i.e. they both have eigenvalue 2) things get slightly more interesting, but not really.