As per the title of the question, what are the matrix elements of the special orthogonal group $SO(4)$? I'm not certain but I believe they are somehow related to being operators of angular momentum denoted by $\hat{L}_i, \hat{L}_j, \hat{L}_k, \hat{L}_m$.
2026-03-28 10:17:14.1774693034
Regarding matrix representation of $SO(4)$
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$SO(4)$ is the group of rotations about the origin in $4$-dimensional space. See this.