The following MATLAB function produces the Eigenvalues and Eigenvectors of matrix X.
[V,D] = eig(X) produces a diagonal matrix D of eigenvalues and a full matrix V whose columns are the corresponding eigenvectors so that X*V = V*D.
My questions are:
- Does this mean that the first (or principal or dominant) eigenvector lay on the last column of V? NOTE: the author says that, all the coefficients of the dominant eigenvector are positive and that the remaining eigenvectors (the rest of columns) must have components that are negative, in order to be orthogonal (what does this mean) to u^(i);
- Regarding the "corresponding eigenvecrtors", do we read them "column-by-column" OR "row-by-row"?
- Do eigenvalues-eigenvectors come in pairs? If yes, and considering the above, then does the corresponding eigenvalue lay on the bottom-right of matrix D?
- Actually, I want eigenvalues and their corresponding eigenectors in decreasing order, and then select the, 2 say, "most significant" ones. What I should do?
- Out of curiosity, but what does it mean "the two times-series Fi and Fi' are uncorrelated in the sense that their empirical correlation vanishes for i != i' ??? How to check that in MATLAB?
LOTS of questions, I know, but I would REALLY appreciate if you could help me answer some of them!