The Rotation Group SO(3)
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We are now going to see how the geometry of physical space is related to its rotations. This allows us to understand angular momentum as a topic in geometry. This is part of a larger program of understanding various physics theories in terms of geometry, including spin in Chapter 14. Often this is achieved by finding a Lie group of symmetries associated with the theory. In this chapter we study the geometry and linear algebra of the Lie group SO(3) and how that is related to angular momentum. Familiarity with matrices (especially matrix multiplication, determinants, and traces) is assumed.