The Lie Algebra is equipped with a bracket notation, and this bracket produces skew symmetric matrices. I know that there exists Lie Groups, one of which is SO(3). And I know that by exponentiating a skew symmetric matrix, I obtain a rotation matrix. ----------------- First, can someone edit the following and say it correctly and with precision (I am not certain I am saying it correctly and the phrasing matters to me) "If one exponentiatiates a MEMBER of the Lie ALgebra, one obtains a member of the Lie Group SO(3)." Could you fix that sentence for me? Second... I get the idea the angular velocity matrices are skew symmetric. I get the idea that rotations are orthogonal. But does this act of exponentiating a skew symmetric matrix imply a one to one correspondence between a specific angular velocity and a rotation? What does that imply? WHAT IS IT about the philosophy (is that a good word? theory? )of exponentiating a matrix that enables this connection between Lie Groups and Lie Algebras? What is it about the fact that we are using a function whose derivative is itself, that causes rotations and angular velocities to be connected (is connected a good word?)?