Revision as of 20:37, 2 August 2021 edit 170.231.46.65 (talk) Edited the examples section to make it clear that the z-rotation matrix works for any angle while the example with 16.26 degrees is just one possibility. Also made sure to use the correct symbol for approximation. Tag: Visual edit ← Previous edit		Revision as of 07:08, 16 November 2021 edit undo Jonas.esc (talk \| contribs) 3 edits →‎Lie algebra Tag: Reverted Next edit →
Line 222: In Lie group terms, this means that the [[Lie algebra]] of an orthogonal matrix group consists of [[skew-symmetric matrix\|skew-symmetric matrices]]. Going the other direction, the [[matrix exponential]] of any skew-symmetric matrix is an orthogonal matrix (in fact, special orthogonal). For example, the three-dimensional object physics ~~calls~~called [[angular velocity]] is a differential rotation, thus a vector in the Lie algebra {{math\|<math>\mathfrak{so}</math>(3)}} tangent to {{math\|SO(3)}}. Given {{math\|1='''ω''' = (''xθ'', ''yθ'', ''zθ'')}}, with {{math\|1='''v''' = (''x'', ''y'', ''z'')}} being a unit vector, the correct skew-symmetric matrix form of {{math\|'''ω'''}} is :<math>

Orthogonal matrix: Difference between revisions