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...Physics a fall eigenvalues and eigenvectors of rotation matrices these notes are supplement to previous class handout entitled in two three many dimensions we shall focus on the proper improper cited above showed that most general matrix is form r cos sin where which represents counterclockwise by an angle x y plane consider eigenvalue problem v since rotates vector conclude for mod there no real solutions eq this can be easily checked explicit calculation as follows det i yields characteristic equation simplies isin e thus ave conrmed not if special cases corresponding respectively obtain expected particular case corresponds dimension inversion implies doubly degenerate equal rotations more interesting noted expressed product reection however it easy show action equivalent pure through line passes origin seen considering wecan again determine solving its interpretation result immediate when operating have means lies parallel unaected perpendicular transformed one therefore computing e...