Eigenvalue & Eigenvector

• Reyleigh Quotient Minimization
• https://www.youtube.com/watch?v=P7yXAPFrXX4
  • For a vector, all the invariants under rotation (change of coordinates) can be expressed as function of the vector's magnitude. i.e. magnitude of a vector is the basis for invariants
  • For a second order tensor (i.e. matrix), its eigenvalues are the basis of the invariants. This is why I think eignevalues come up so often everywhere. Because they are independent of the coordinates system we take.