Topics: Eigenvalues and Eigenvectors - Algebra


Let and let be an eigenvalue of . We define:

…and call this set the eigenspace that corresponds to the eigenvalue.


is a vector subspace that contains and the eigenvectors of that correspond to .

The number of linearly independent eigenvectors of is the dimension of .


Let be a linear operator on a vector space with finite dimension.

If is an eigenvalue of with multiplicity, then: