Lie Algebra
See also: Infinitesimal rotationSince SO(3) is a Lie subgroup of the general linear group GL(3), its Lie algebra can be identified with a Lie subalgebra of gl(3), the algebra of 3×3 matrices with the commutator given by
The condition that a matrix A belong to SO(3) is that
- (*)
If A(t) is a one-parameter subgroup of SO(3) parametrised by t, then differentiating (*) with respect to t gives
and so the Lie algebra so(3) consists of all skew-symmetric 3×3 matrices.
Read more about this topic: Rotation Group SO(3)
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