41. Birkhoff factorization implies the Birkhoff Grothendieck theorem of that vector bundles over the projective line are sums of line bundles. 42. Accordingly, the general linear group of 2 & times; 2 invertible matrices acts on the real projective line . 43. The complex analog of the real projective line is the complex projective line; that is, the Riemann sphere. 44. The complex analog of the real projective line is the complex projective line ; that is, the Riemann sphere. 45. In the case of a complex projective line , or the Riemann sphere, these transformation are known as M�bius transformations. 46. And the projective line is not totally ordered . talk ) 06 : 44, 8 January 2006 ( UTC) 47. A distinction between the terms arose when the distinction was clarified between the real projective plane and the complex projective line . 48. In quantum mechanics, points on the complex projective line are natural values for photon relativistic model for the celestial sphere. 49. Either of or may be zero, but not both, so both charts are needed to cover the projective line . 50. This equation has regular singularities at 0 and " in the projective line "'P "'1.
