WHY eigenvectors/eigenvalues are important

• Simplification:

  • When you find eigenvectors and eigenvalues, you simplify an entire, complicated transformation into a set of simple stretches or compressions along independent directions.

flowchart TD
   Mass1[(Mass1)]
   Mass2[(Mass2)]
   Wall1@{ shape: trap-t, label: "Wall", animate: true }
   Wall2@{ shape: trap-b, label: "Wall", animate: true }
   Wall1 e1@o==|Spring|==o Mass1
   Mass1 e21@o==|Spring|==o Mass2   
   Mass2 e22@o==|Spring|==o Mass1
   Mass2 e3@o==|Spring|==o Wall2

  classDef animate stroke-dasharray: 1 4, stroke-dashoffset: 10, animation: dash 0.5s alternate-reverse infinite ease, stroke: gold;
  class e1 animate
  class e21 animate
  class e22 animate
  class e3 animate