In Lie group terms, this means that the Lie algebra of an orthogonal matrix group consists of skew-symmetric matrices. Going the other direction, the matrix exponential of any skew-symmetric matrix is an orthogonal matrix (in fact, special orthogonal).
I am not sure what this would mean. So, the elements that go into "lie bracket" consists of only skew-symmetric matrices? I am very confused here, and can anyone explain this?