Rotation Group SO(3) - Lie Algebra

Lie Algebra

See also: Infinitesimal rotation

Since 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:

    For six years you shall sow your land and gather in its yield; but the seventh year you shall let it rest and lie fallow, so that the poor of your people may eat; and what they leave the wild animals may eat. You shall do the same with your vineyard, and with your olive orchard.
    Bible: Hebrew, Exodus 23:10,11.

    Poetry has become the higher algebra of metaphors.
    José Ortega Y Gasset (1883–1955)