Eigenvalues

• How to Calculate an Eigenspace
  Calculate an eigenspace by solving the homogeneous system (A − λI)x = 0, then express its solution set as a span or basis.
• Can One Eigenvalue Have Two Different Eigenvectors?
  Yes. An eigenvalue can have many eigenvectors: every nonzero vector in its eigenspace qualifies, including scalar multiples and, sometimes, independent vectors.