What does "The corollary of this is that ..." mean? In such context: We now come to the geometric interpretation of 3D rotations. We can think about the rows of the matrix as being unit vectors of a new coordinate frame. So, we can think of this as being the u vector, the v vector, the w vector, where x_u is the X coordinate of the u vector, y_u is the Y coordinate of the u vector, and z_u is the Z coordinate of the u vector. Similarly for the v vector and the w vector. When I say the u vector is the axis of the new coordinate frame, the vector u will be equal to x_u times the X direction plus y_u times the Y direction, plus z_u times the Z direction. The corollary of this is that given 3 orthonormal vectors, and orthonormality means that, this u vector dot with v vector has to be equal to 0, u vector dot with w vector has to be equal 0, v dot w has to be equal to 0, and u, v and w are unit vectors. Thanks.