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