Talk:Linear Algebra/Eigenvalues and Eigenvectors

Has 'kernel' been defined already in this text?
I'd like to recommend the Eigen* page to some non-math students who need a reference (and problem set), but the use of the kernel in the middle would confuse them at a vital point. My searching doesn't turn up a definition that would be useful to a early student. Pointer?

128.32.27.136 (talk) 19:41, 29 October 2010 (UTC)

Lemma 3.10
I think this lemma is flawed. Nothing forbids that the root of the characteristic polynomial be an eigenvalue associated with a 0 eigenvector (in which case one doesn't speak of an eigenvalue). This is indeed what happens when one tries to find eigenvalues of nilpotent matrices. Wisapi (discuss • contribs) 19:23, 3 August 2011 (UTC)


 * Nope, the lemma is right. Taking the determinant of the matrix to be 0 --in other words, making it singular-- ensures that the eigenvector is not trivial. Only if the determinant were not zero, there would be only one eigenvector (and not a nontrivial set) associated to the eigenvalue. Wisapi (discuss • contribs) 00:48, 4 August 2011 (UTC)