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That’s because skew-symmetric matrices are the Lie algebra of the Lie group of rotation matrices (and the exponential map takes a Lie algebra to a Lie group). I
by senderista 8y ago
That’s because skew-symmetric matrices are the Lie algebra of the Lie group of rotation matrices (and the exponential map takes a Lie algebra to a Lie group). In physics we call them the “infinitesimal generators” of the rotation group.
- gugagore 8y agoI love knowing about Lie algebras and groups, but I think I disagree about the "because". The matrix exponential and logarithm just are. You can define and compute them without invoking anything about Lie groups. I didn't know the term "infinitesimal generator". Thanks!