sentences:  If is a vector in R3, then we identify "X" with the 2 × 2 matrix with complex entries
  
  Note that −det("X") gives the square of the Euclidean length of "X" regarded as a vector, and that "X" is a trace-free, or better, trace-zero Hermitian matrix.The unitary group acts on "X" via
  
  where "M" ∈ SU(2).Note that, since "M" is unitary,
  
  Hence SU(2) acts via rotation on the vectors "X".