Eigenvector mystery

[JurgenRo]

(10-19-2020 07:13 PM)Albert Chan Wrote:  

(10-18-2020 10:54 PM)pinkman Wrote:  Eigenvalues (w) and eigenvectors (v) of a matrix (M) belong inseparably together and define each other: Mv=wv.

True, but so is M(kv) = w(kv)

For eigenvalue w, all kv are valid eigenvectors for it, as long as k ≠ 0

Also true but not relevant It's all about to pick a set of linear indpendent Eigenvectors for a certain Eigenvalue, i. e. a base for the corresponding Eigenspace.