LagrangeEuler
- 711
- 22
What is the basis of 2x2 matrices with real entries? I know that the basis of 2x2 matrices with complex entries are 3 Pauli matrices and unit matrix:
\begin{bmatrix}<br /> 0 & 1 \\[0.3em]<br /> 1 & 0 \\[0.3em]<br /> \end{bmatrix},
\begin{bmatrix}<br /> 0 & -i \\[0.3em]<br /> i & 0 \\[0.3em]<br /> \end{bmatrix}
\begin{bmatrix}<br /> 1 & 0 \\[0.3em]<br /> 0 & -1 \\[0.3em]<br /> \end{bmatrix}
and
\begin{bmatrix}<br /> 1 & 0 \\[0.3em]<br /> 0 & 1 \\[0.3em]<br /> \end{bmatrix}
What about in the case of real 2x2 matrices? How many matrices is there in the basis?
\begin{bmatrix}<br /> 0 & 1 \\[0.3em]<br /> 1 & 0 \\[0.3em]<br /> \end{bmatrix},
\begin{bmatrix}<br /> 0 & -i \\[0.3em]<br /> i & 0 \\[0.3em]<br /> \end{bmatrix}
\begin{bmatrix}<br /> 1 & 0 \\[0.3em]<br /> 0 & -1 \\[0.3em]<br /> \end{bmatrix}
and
\begin{bmatrix}<br /> 1 & 0 \\[0.3em]<br /> 0 & 1 \\[0.3em]<br /> \end{bmatrix}
What about in the case of real 2x2 matrices? How many matrices is there in the basis?