Discovering Group Theory, Day 18

On Day 18, we returned to the spacetime symmetries we discussed last time, but treated them with a bit more rigor and tighter notation.  In the context of the Newton’s 2nd law, we worked out the math for

  • Translation group as applied to three-dimensional space and to time.
  • Rotations in space and their matrix representation in 2D.
  • We formally defined the orthogonal group O(2) and the special orthogonal group SO(2).