I am given the following set of 4x4 matrices. How can i justify that they form a basis for the Lie Algebra of the group SO(4)? I know that they must be real matrices, and [itex]AA^{T}=\mathbb{I}[/itex], and the [itex]detA = +-1.[/itex] Do i show that the matrices are linearly independent, verify these properties, and so they are a basis? Why are they 6 elements?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

_{A_1}=\begin{pmatrix}

0 &0 &0 &0 \\

0 & 0 & 1 & 0 \\

0& -1 &0 &0 \\

0& 0& 0 & 0

\end{pmatrix}

,\\

\

_{A_2}=\begin{pmatrix}

0 &0 &-1 &0 \\

0 & 0 & 0 & 0 \\

1& 0 &0 &0 \\

0& 0& 0 & 0

\end{pmatrix}

,\\

_{A_3}=\begin{pmatrix}

0 &-1 &0 &0 \\

1 & 0 & 0 & 0 \\

0& 0 &0 &0 \\

0& 0& 0 & 0

\end{pmatrix}

\\

_{B_1}=\begin{pmatrix}

0 &0 &0 &-1 \\

0 & 0 & 0 & 0 \\

0& 0 &0 &0 \\

1& 0& 0 & 0

\end{pmatrix}

,\\

_{B_2}=\begin{pmatrix}

0 &0 &0 &0 \\

0 & 0 & 0 & -1 \\

0& 0 &0 &0 \\

0& 1& 0 & 0

\end{pmatrix}

,\\

_{B_3}=\begin{pmatrix}

0 &0 &0 &0 \\

0 & 0 & 0 & 0 \\

0& 0 &0 &1 \\

0& 0& -1 & 0

\end{pmatrix}

[/tex]

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# A Justify matrices form basis for SO(4)

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