Recent content by oldmathguy

Fredrik, Thanks very much for clarifying SO(3, R) using Euler angles. I somewhat understand Euler angles so can see why 3 work. I found some another good explanation of the dimension of SO(3) by Prof. VVedensky from Imperial College...

Fredrik, Thanks for clarifying this. Since a 3-dim. manifold, what do its 3 dimensions represent? By this, I mean are they the rotation matrices (or angles) for rotations about three orthogonal axes ? SE(3,R) & GL+(3,R) also are Lie groups so how does one get dimensions of these manifolds...

Fredrik, Thanks for your comment. Sorry for not being clearer. I mean the dimension of the vector space of 3 X 3 matrices R in SO(3, R). In other words, the number of elements in the basis. SO(3,R) is nxn real matrices such that RR^T = I & detR = 1. I think that the answer is 3 but I'm...

I have a similar question about rotation matrices. I'm trying to understand the dimension of the matrix given below which is a 3-D rotation. I think that its dimension is 3 but unsure. Any help appreciated. Thanks, John [(cosx sin x 0), (-sinx cosx 0), (0 0 1)] with ( ) = row,

They're equal ! Col Rank (A) = Row Rank (A^T) so dim (A) = Col Rank (A) = Row Rank (A^T) = Rank (A^T). Thanks ! John.

Hi, I'm new to the forum but have watched it for some time. I am trying to prove that Rank (A^T) = Rank (A) with A being mxn matrix. I suspect that it has to do with Rank (A) = Row Rank (A) = Column Rank (A) -and- A^T simply being rows / columns transposed but am unsure how to prove. Thanks, John.