Can someone please explain what an eigenspace is? I think I have a rough idea of it but am still uncertain.

Question

jim_thompson5910 · Answer

An eigenspace of some eigenvalue λ is a subspace where the basis vectors are {x1,x2,...,xn} which are the n eigenvectors corresponding to λ.


Put another way, λ is an eigenvalue if   Ax = λx and x is the eigenvector, keep in mind that λ is a scalar.

anonymous · Answer

but in the case of eigenspace, is the scalar fixed? cause there are some notes of mine which says that it is a fixed scalar.

jim_thompson5910 · Answer

yes, the scalar is fixed and the eigenspace depends on it (ie if you change the scalar, the eignenspace may change)

note: you can have multiple eigenvalues

anonymous · Answer

oh ok. i understand now. thanks (: