Worked Problems in Physics

Nielsen and Chuang Exercise 2.36

Posted in Nielsen/Chuang by rpmuller on March 11, 2010

Exercise 2.36 Show that the Pauli matrices except for {I} have trace zero.

\displaystyle  \mathrm{tr}\left[ \begin{array}{rr} 0 & 1\\ 1 & 0 \end{array} \right] = 0+0 = 0

\displaystyle  \mathrm{tr}\left[ \begin{array}{rr} 0 & -i\\ i & 0 \end{array} \right] = 0+0 = 0

\displaystyle  \mathrm{tr}\left[ \begin{array}{rr} 1 & 0\\ 0 & -1 \end{array} \right]=1-1=0