L1-a.dvi

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1 27 Q C [ ] cosθ sinθ. A θ < 2π sinθ cosθ A. A ϕ A, A cosϕ cosθ sinθ cosθ sinθ A sinθ cosθ sinθ +cosθ A, cosθ sinθ+sinθ+cosθ cosθ A 2 A,A cosθ sinθ 2 +sinθ +cosθ 2 2 cos 2 θ+sin 2 θ+ 2 sin 2 θ +cos 2 θ , cosϕ A, A cosθ cosθ ϕ π θ π ϕ θ π θ < 2π cosϕ cosθ cos2π θ < 2π θ π ϕ 2π θ A θ s t z L. A, B, z u v w A+z A+Az, 2 A+B A+B L z L3., z w z θ,z z cosθ L4. A deta ad bc a, b 2 deta L5. A a, b deta,,, a+b

2 2 27 Q C. L. A s t, B u v A+z A+Az, A+B A+B z, z w +z +z +w A+z +z +w a+z+b +w c+z+d +w a+b A c+d z az +bw Az w cz +dw A+Az a+b + c+d az +bw cz +dw 2 A+B A+B + a+s b+t c+u d+v s t u v a+z+b +w A+z c+z+d +w a+s b+t c+u d+v a+s+b+t c+u+d+v a+b A c+d s t s+t B u v u+v A+B a+b s+t a+s+b+t + A+B c+d u+v c+u+d+v

3 27 Q C 3 L L3., z z z θ w,z z cosθ z,z z z,z z cosθ, z, z z 2 + z 2 z 2 2 z cosθ z, z w 2, z 2 z,z z 2 +w 2

4 4 27 Q C z z w z 2 z, z z 2 + w z 2 z z 2 +w 2 z 2 w 2 2z+w 2,z,z z cosθ L4. A deta ad bc a, b deta 2 S a b a b S ad, bc c d S ad bc a b a b θ S S a b sinθ a a, b a 2 a,a a 2 +c 2 b 2 b,b b 2 +d 2 S 2 a 2 b 2 sin 2 θ a 2 +c 2 b 2 +d 2 cos 2 θ a, b L3 cosθ a,b a b a 2 b 2 cos 2 θ a,b 2 ab+cd 2

5 27 Q C 5 S 2 a 2 +c 2 b 2 +d 2 cos 2 θ a 2 +c 2 b 2 +d 2 ab+cd 2 a 2 b 2 +a 2 d 2 +c 2 b 2 +c 2 d 2 a 2 b 2 +2abcd+c 2 d 2 a 2 d 2 +c 2 b 2 2abcd ad bc 2 S ad bc a L5. A a c b, b d,,, a+b deta deta ad bc ad bc a d bc a b, a a+b b ab ab a bc c a bc c a a ad bc ad b c c a, a+b a c b d, c a+b d +c c d dc+cd

6 6 27 Q C. A s t B u v A+B a+s b+t c+u d+v A k R ka ka kb kc kd 2 2 a +b 2 2 c +d 2 A f f A a +b A 2 c +d 2 a A A b a +b 2 A 2 A 2 2 c +d 2 A a +b 2 2 a +b 2

7 27 Q C 7 [ ] cosθ sinθ. Aθ sinθ cosθ AθAϕ Aθ+ϕ. cosθ sinθ cosϕ sinϕ Aθ, Aϕ sinθ cosθ sinϕ cosϕ cosθ sinθ cosϕ sinϕ AθAϕ sinθ cosθ sinϕ cosϕ cosθcosϕ sinθsinϕ cosθsinϕ sinθcosϕ sinθcosϕ+cosθsinϕ sinθsinϕ+cosθcosϕ cosθ +ϕ sinθ +ϕ Aθ+ϕ sinθ+ϕ cosθ+ϕ Aθ θ Aθ Aϕ ϕ θ AθAϕ θ+ϕ k L6. k R I P, Q, k R A IA, PA, QA, RA. 2 AI, AP, AQ, AR. L7. A deta ad bc X d b AX I XA I X A deta c a L8. A deta, c A A c L9. 3, L. A A 2 a+da+ad bci O

8 8 27 Q C. k L6. k R I P, Q, k R A IA, PA, QA, RA. 2 AI, AP, AQ, AR. a+ c b+ d IA a+ c b+ d a+ c b+ d PA a+ c b+ d k k a+ c k b+ d ka kb QA a+ c b+ d k a+k c b+k d a+kc b+kd RA a+ c b+ d 2 a +b a +b AI c +d c +d a +b a +b b a AP c +d c +d d c k a k +b a +b k AQ c k +d c +d k k a +b a k +b a ka+b AR c +d c k +d c kc+d IA AI L7. A d b deta c a PA AP, QA AQ, RA AR deta ad bc X AX I XA I X A

9 A B 27 Q C 9 d b c a d b ad+b c a b+ba ad bc AB c a cd+d c c b+da ad bc d b da+ bb+ bd ad bc BA c a ca+ac cb+ad ad bc AX A XA ad bc B ad bc AB ad bc BA ad bc ad bc ad bc ad bc I ad bc ad bc I L8. A deta, c A A c A c L7 A A A I A A A A I I A c I + + A c A c A c A c A c AA I A c A AA c AA c Ic c A c A c A A c

10 27 Q C L9. 3, 2 2 A 3, c 2 L8 A c 2 5 deta A, c 2 5 L8 A c 2 deta L. A A 2 a+da+ad bci O A 2 A A A 2 a2 +bc ab+bd ca+dc cb+d A 2 a+da+ad bci a+d +ad bc a2 +bc ab+bd ca+dc a+da a+db ad bc + cb+d 2 a+dc a+dd ad bc a 2 +bc a+da+ad bc ab+bd a+db ca+dc a+dc cb+d 2 a+dd+ad bc O

11 27 Q C. s t A, B u v A a+b c+d s t a+b BA BA u v c+d sa+b+tc+d ua+b+vc+d sa+tc+sb+td ua+vc+ub+vd sa+tc sb+td ua+vc ub+vd BA sa+tc sb+td ua+vc ub+vd BA i,j B i A j s t BA u v a A a, a c 2 Ba 2 sa+tc sb+td ua+vc ub+vd b BA Ba d, 2

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