"T is a linear operator on a fin-dim vector space V
Beta is an ordered basis for V
Prove that Lambda is an eigenvalue of T iff Lambda is an eigenvalue of [T](subBeta)"
"T is a linear operator on a fin-dim vector space V
Beta is an ordered basis for V
Prove that Lambda is an eigenvalue of T iff Lambda is an eigenvalue of [T](subBeta)"
Let be a linear transformation with and eigenvalue, so for some .
Let be the corresponding matrix with respect to this ordered basis .
Remember that where is the coordinate with respect to .
Since .