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Pauli matrix

  1. May 12, 2012 #1
    Why is norm of (pauli matrix)/sqrt(2)=1
     
  2. jcsd
  3. May 12, 2012 #2

    HallsofIvy

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    Which "Pauli matrix" are you talking about? My first thought was the "Pauli matrices" used in quantum mechanics:
    [tex]\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}\begin{pmatrix}0 & -i \\ i & 0\end{pmatrix}[/tex]
    but they all have determinant -1.
     
  4. May 12, 2012 #3

    Fredrik

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    The set of Pauli matrices is a basis for the (real) vector space of complex traceless self-adjoint 2×2 matrices. If we define the inner product on that space by ##\langle A,B\rangle=\operatorname{Tr}(A^*B)##, where * denotes conjugate transpose, then I think the matrices ##E_i=\sigma_i/\sqrt{2}## form an orthonormal basis of that space. (You should check to make sure that I remember this right).
     
  5. May 13, 2012 #4

    HallsofIvy

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    Ahh! so the key point is that for every Pauli matrix, A, A*A= the 2 by 2 identity matrix that has trace 2.
     
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