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--- mvg:lecture_03:start [2018/11/29 14:03] – [TRansformation between Lie Algebra and Lie Group] admin
+++ mvg:lecture_03:start [2018/12/23 18:45] (current) – [TRansformation between Lie Algebra and Lie Group] admin
@@ Line 77: / Line 77: @@
 The Lie algebra $so(3)$ is the tangent space at the identity of the rotation group $SO(3)$
+algebra over a field K is a vector space over K with multiplication on the space V. Not commutative.
 Lie Brackets:
-$\left[\hat{w},\hat{v}\right] \ident \hat{w}\hat{v}-\hat{v}\hat{w}$
+$\left[\hat{w},\hat{v}\right] \identical \hat{w}\hat{v}-\hat{v}\hat{w} \in so(3)$
+Two Lie groups we will study: $so(3), se(3)$
+=== Exponential Map ===
+$\left\{ \dot{R}(t)=\hat{w}R(t)\right. $
+$R(0) = I$
+How does the rotation matrix change from one time within a little time step?
+$R(t) = e^{\hat{w}t} = \sum \ldots $ expansion. That solves the diff. eqn. above.
+$\exp: so(3) \rightarrow SO(3)\quad \hat{w} -> e^{\hat{w}}$
-Two Le groups we will study: $so(3), se(3)$