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)
Famous quotes containing the words lie and/or algebra:
“Although Id lie lapped up in linen
A deal Id sweat and little earn
If I should live as live the neighbours,
Cried the beggar, Billy Byrne....”
—William Butler Yeats (18651939)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (18831955)