[FONT=CMR12][LEFT]What is eigenspace? this may seem like a general question but i cant find it online. I understand how to find the basis and eigenvectors, but im lost as to what the eigenspace is.
Here is the question that i am stuck on
Given that the eigenvalues of M =
2 -5 5
0 3 -1
0 -1 3
are 2, 2 and 4.
(a) Find the eigenspace corresponding to the eigenvalue 2. What is its dimension?
Mar 28th 2010, 04:41 PM
the eigenspace of an eigenvalue is the space generated by the eigenvectors coresponding to that eigenvalue. if an eigenvalue has multiplicity greater than 1, its eigenspace can also have a dimension greater than one. in your case finding the eigenspace of 2 is the same as finding a basis for the nullspace of