The first applicable complex imaginary square matrices were 2 by 2 Pauli matrices of quantum mechanics. Then in quantum field theory or quantum electrodynamics (QED) the Dirac matrices were 4 by 4 complex imaginary square matrices. Then in quantum chromodynamics (QCD) Gell-Mann matrices were 3 by 3 complex imaginary square matrices. Now, a quantum theory of the spacetime continuum can be described by 2 by 2 real square symmetric Hadamard matrices representing infinitesimal double spin rotations. Their advantage is commutativity of matrix multiplication. Their disadvantage is singularity. However, the zero power of Hadamard matrices gives the identity matrix.