Email: huangzh@whueducn, 47 Wuhan Univesity
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: : 4 ; 8 a b c ; a b c 4 4 8 a b c b c a ; c a b x y x + y y x + y x x + y x y 4 + + 8 8 4 4 + 8 + 6 4 4 a b c b c a acb + bac + cba bbb aaa ccc abc a b c c a b a b c bc + ca + ab ac ba cb a bb cc a a b c 4 x y x + y y x + y x x + y x y xx + yy + yxx + y + x + yyx y x + y x xyx + y y x y y x x y x x + y, : 4; 4 ; 4 ; 4 4 ; 5 n 4 n; 6 n n n 4: 4, 4, 4, 5:,, 4, 4, 4 :, 4, 4 5 nn :
5, 5 4 7, 7 4, 7 6 n, n 4, n 6,, n n n 6 nn : 5, 5 4 7, 7 4, 7 6 n, n 4, n 6,, n n n 4 6, 6 4 n, n 4, n 6,, n n n a a :, t p p p p 4 t a p a p a p a 4p4, p, p, p p p p 4, 4 4 t, a a a a 44 a a a 4 a 4 + + +, + + + 4 : 4 4 4 5 ; ; 7 5 6 a ab ac ae bd cd de ; 4 b c bf cf ef d : 4 4 5 4 4 4 5 7 4 5 7 7 7 4 7 4+7 5 7 +5 7 85 7 9 7 5 7 4 9 45 5
+ 4, ab ac ae b c e bd cd de adf b c e adfbce bf cf ef b c e + adfbce + adfbce 4abcdef 4 a + ab a b +a c b c d d + ab a + ab a ad + c c +dc c + cd d + ab ad + abcd + ab + cd + ad + + cd 5 : x + x + ; x + : x + x + x + c +c x + x + x + x + x x + x + x + x, x + x x + x,, x a b c x a b c, a, b, c x a b c :, c bc ab ac xb xa x, x a, b, c x a,,, x a x b, x c, x a, b, c 6 : a ab b a a + b b a b ;
4 a ab b a ab a b a a a + b b c c c c a b a b a + ab a b a a b + a b ab a b a b a a b ax + by ay + bz az + bx x y z ay + bz az + bx ax + by a + b y z x ; az + bx ax + by ay + bz z x y : ax + by ay + bz az + bx x ay + bz az + bx y ay + bz az + bx ay + bz az + bx ax + by a y az + bx ax + by + b z az + bx ax + by az + bx ax + by ay + bz z ax + by ay + bz x ax + by ay + bz x ay + bz z y z az + bx a y az + bx x + + + b z x ax + by z ax + by y x y ay + bz x y z y z x a y z x + b z x y z x y x y z x y z x y z x y z a y z x + b y z x a + b y z x z x y z x y z x y : ax + by ay + bz az + bx ax ay az ay + bz az + bx ax + by ay az ax az + bx ax + by ay + bz az ax ay x y z y z x x y z a y z x + b z x y a y z x z x y x y z z x y x y z a + b y z x z x y by bz bx + bz bx by bx by bz x y z + b y z x z x y,!, : a a n b b n a + b a n + b n + a n a nn b n b nn a n + b n a nn + b nn a a + a + a + b b + b + b + c c + c + c + d d + d + d + ;
5 : a a + a + a + a a + 4a + 4 6a + 9 b b + b + b + c j c c c + c + c + b b + 4b + 4 6b + 9 j,,4 c c + 4c + 4 6c + 9 d d + d + d + d d + 4d + 4 6d + 9 a a + 6 c c b b + 6 c 4 c c c + 6 d d + 6 4 a b c d a b c d a ba ca db cb dc da + b + c + d; a 4 b 4 c 4 d 4 : a b c d c j c a b c d a b a c a d a j,,4 a b a c a d a a 4 b 4 c 4 d 4 a 4 b 4 a 4 c 4 a 4 d 4 a 4 b a c a d a b a c a d a b b a c c a d d a b ac ad a b + a c + a d + a b b + a c c + a d d + a c c b ac ad a c c b + a c b d b b b + a c c + a b b + a d d + a b b + a b ac ad ac bd b c + bc + b + ac + b d + bd + b + ad + b a ba ca db cb dc da + b + c + d x x 5 x n + a x n + + a n x + a n x a n a n a n a x + a : x, x x D n x x a n a n a n a a x + a
6 x x c n +xc n x a n a n a n a x + a x + a x + a x x c n +xc n a n a n a n x + a x + a x + a x + a x + a x + a c j+xc j x n + a x n + + a n x + a n x n + a x n + + a n x + a n x + a x + a x + a x n + a x n + + a n x + a n n+ x n + a x n + + a n x + a n n+ n x n + a x n + + a n x + a n n n, x, D n a n x, D n x x c + x c x a n a n + an x a n a x + a x x c + x c x a n a n + an x a n + an x + an x a x + a
7 x x x a n a n + an x a n + an x + an x P P,, P a + a x + a 4 x + + + a n x n, P x + a + a x + a x + + + a n x n D n x n P x n + a x n + + a n x + a n D n x x x a n a n a n a x + a, x D n c x x a n a n a x + a + a n n+ x x, D n xd n + a n xd n + a n n+ n xd n + a n D n x n + a x n + + a n x + a n a n i D n x x x x x x x a n a n a n a n i a n i a n i+ a x + a a n i, i i, n i n i,
8 a n i a n i n i + n+i+ x x x x i i x x n i n i x i, D n, D n a n + a n x + a n x + + a n i x i + + a x n + x + a x n x n + a x n + + a n x + a n c D n x x x x a n a n a n a x + a c +xc x x x x a n + a n x a n a n a x + a c +x c x x x x a n + a n x + a n x a n a n a x + a x x x P a n a n a x + a,, P a n + a n x + a n x + + a x n + x n, D n x n + a x n + + a n x + a n
9 7 n D det a ij, D 9, a n a nn a n a nn a nn a n D, D, D, a a n a a n a n a D D nn D, D D : a n a nn a a n D n n a n a nn n a a n a a n a a n a a n n n n a n a nn n a a n a a n n n ++ +n +n D nn D a n a nn D nn a a n a n a nn nn D T nn D D nn D nn nn D nn D D 8 D k k a D n, a, ; a : c n n, : a a a a D n n a a a a n n, : a a D n n n a a a a a a n n a a n
D n a a a a c a a a n n + n+ a a n n a n + n+ n + a a n n a n a n D n x a a a x a a a x ; :, D n x a a a a x x a a x x a a x x a,, D n x + n a a a a x a x a x a [ x + n a ] x a n D n x + n a a a x + n a x a x + n a a x [ x + n a ] a a x a a x
, a a a D n [ x + n a ] x a x a x a [ x + n a ] x a n a a a x a a D n a x a a a x n+ n+ i i,, a a a x a x a x a n+ n+ x a, D n x a, x a c j c, j,,, n + : D n + a x a n a a a x a x a + na x a n+ n+ x a x a n [ x + n a ] x a n a n a n a n n a n a n a n n D n+ ; : a a a n : n +, n + n, ; n n n + n + + nn+, 6 a a a n D n+ nn+, a n a n a n n a n a n a n n, a x, a x,, a n x n, a n x n+ x i a i, x j a j D n+ nn+ nn+ n+i>j n+i>j xi x j [ a i + a j + ]
nn+ n+i>j [ i j ] nn+ n+n + + n+i>j i j n+i>j i j : 8 9, 6, D n+ a n a n a a n n n a n a n a n n n a n a n,, x a n, x a n +, x a n +,, x i a n + i, x i x j i j, D n+ n+i>j a n b n a b 4 D n ; c d c n d n : xi x j n+i>j i j : c n n, ; n n, a n b n c n d n a n b n D n n n a b a n d n b n c n D n, c d c n d n n D a b c d a d b c, n D n a n d n b n c n a d b c a i d i b i c i i P5
D n an a n b n a b c d c n d n d n + n+ b n a n bn a b c d c n d n c n n an d n D n b n c n D n : D n a n d n b n c n D n, n D n a i d i b i c i D i a b n D c d a d b c, D n a i d i b i c i i Laplace, 5 D n deta ij, a ij i j ; : a ij i j n n n D n deta ij n n n 4 n 5 n n n n 4 i i+ i,, n n n n 4 c j+c j,, n n n 4 n 5 n 6 D n n n n + a + a, a a a n + a n
4 : + a D n + a + a n a i a i,, a n n+ n+ + a a c + a c a a n n+ n+ + a + a + + a n a c + a c j+ j a a n n a a a n + a i j,, i n+ n+ n+ n+ 9 D 5 4 5, D i, j A ij, A + A A + A 4 : 5 4 5,, A + A A + A 4 5 4 5 4
5 : x + x + x + x 4 5, x + x x + 4x 4, x x x 5x 4, x + x + x + x 4 ; : D 4 5 5 7 8 8 5 4 4 8 5 4 5 5 5 5 D 4 5 5 5 8 5 8 5 8 4 4; 5 8 5 5 5 D 4 5 7 7 9 84; 5 8 9 5 5 D 4 5 46; D 4 4, x D D, x D D, x D D, x 4 D 4 D 5x + 6x, x + 5x + 6x, x + 5x + 6x 4, : x + 5x 4 + 6x 5, x 4 + 5x 5 D 5 5 5D 4 4 6D, 5 6 5 6 6 c D 5 5 5 6 5D4 4 5 6 5 6 5 6 5 5 5 6 5D 4 4 6 5 6 5D 4 4 6D 5 D 5D 6D 55 6 6 5 65, D 4 4 5D 6D 5 65 6 9,
6 D 5 5 5D 4 4 6D 5 6 65 665 D 6 5 6 5 6 5 6 5 c D4 4 + 6 5 6 5 6 5 6 D 4 4 + 6 4 + 6 4 57 5 6 6 c D 5 6 5 6 5 6 5 6 5 5 + 5+ 5 6 5 6 5 6 c D 5 6 65 8 45 5 6 5 5 c D 6 + 6 5 6 5 6 5 5 + 5+ 5 6 5 6 5 6 c D 6 6 D 7 5 6 5 6 c D 4 4 5 +4 6 5 5 6 5 6 5 + 5+4 5 6 5 6 5 6 c 4 5 6D 5 6 65 95 5 6 5 6 5 6 c D 5 5 5 6 +5 5 6 5 5 + 5 6 5 6 5 6 5 + D 4 4 +, x 57 665, x 45 665, x 7 665, x 4 95 665, x 5 665,, λx + x + x, λ, µ, x + µx + x, x + µx + x?
7 : D λ µ µ λ µ µ µ + λ µ λ, D, µ λ, µ λ λx x + 4x, λ, x + λx + x,? x + x + λx : λ 4 λ + λ 4 D λ c c λ λ λ + + λ 4 λ + λ + λ + λ λ λ 4 λ + λ λ + λ λ + λ + λ λλ λ, D, λ, λ λ λλ λ
: 4 7 ;,, ; 5 7, ; 4 4 4 ; 4 a a a x 5 x, x, x a a a x ; a a a x 6 4 7 4 7 + + 5 : 7 + + 6 5 7 5 7 + 7 + 49,, + + 4, 6 4 4 6 7 8 4 5 6 4 5 a a a x, x, x a a a a a a a x + a x + a x, a x + a x + a x, a x + a x + a x x x x x x x a x + a x + a x + a x x + a x x + a x x 8
9 5 6 4 4 9 A, B 4, 5 AB A A T B : AB A 4 5 5 8 5 6 7 9 4 9 A T B 4 5 5 8 5 6 9 x y + y, x y + y + y, x 4y + y + 5y, y z + z, y z + z, y z + z, z, z, z x, x, x : : x y + y z + z + z + z 6z + z + z, x x x y y y 4 5 y y y z z z,, x x x 4 5 y y y 4 5 z z z
6 4 9 6 z z z x 6z + z + z, x z 4z + 9z, x z z + 6z 4 A, B, : AB BA? A + B A + AB + B? A + BA B A B? : 4 AB, BA 4 6 8,, AB BA 8 4 A + B 5 5 4 9, 8 6 8 6 A + AB + B 4 + 8 + 4 5 7, A + B A + AB + B 6 A + BA B 5 9, 8 8 A B 4 4 7, A + BA B A B,, AB BA, A + B A + AB + BA + B A + AB + B, A + BA B A AB + BA B A B 5 : A O, A O; A A, A O A E;
AX AY, A O, X Y : A, A O, A O A, A A, A O A E A, X, Y AX AY A O X Y 5 6,,,,,,,,,,,,, 6 A : λ A, A,, A k A λ λ λ, A A A λ λ λ : A n nλ n, n k, n k + A k+ A k A : A k kλ λ 7 A λ, Ak λ kλ λ : λ λ A λ λ λ λ A A A λ λ λ λ λ λ k + λ λ λ λ λ λ,
: A n : n, λ n nλ n nn λ n λ n nλ n λ n n k, n k + : A k A k+ A k A, n λ k kλ k kk λ k λ k kλ k λ k λ k+ k + λ k k+k λ k λ k+ k + λ k λ k+ λ k kλ k kk λ k λ k kλ k λ k λ λ λ λ A λ + λe + B λ A n λe + B n λe n + C nλe n B + C nλe n B + + B n B, B B k, B, k A n λe + B n λe n + CnλE n B + CnλE n B λ n nλ n λ n + nλ n + λ n C nλ n A, B, A + B n A + B A + AB + B, A, B λe, B
λ n nλ n nn λ n λ n nλ n λ n 8 A, B n, A, B T AB : B T AB T B T AB A T A, AB T B T A T B T AB T B T AB T B T B T A T B T A T B B T AB B T AB 9 A, B n, AB AB BA : A T A, B T B, AB T AB AB BA : AB BA AB T B T A T BA,, AB T AB AB : AB T AB AB T B T A T BA,, AB BA : ; 5 : A, A, A 5 A 5, A, A, A A A A A A 5 A A A P44 : a b c d 5 d b ad cb c a A A A ad cb cos θ sin θ sin θ cos θ ;
4 cos θ : sin θ sin θ cos θ 4 5 4, ; : A, A cos θ sin θ sin θ cos θ cos θ sin θ sin θ cos θ A 4, A, A, A, A 6, A, A, A 4, A a a 4 a n : A A A, a a a n a a a n 6 7 a a a n : 5 4 6 X ; 5 4 6 5 4 6 : X 8 X ; 4 : X 4 4
5 8 5 4 X ; : 4 X 4 6 6 4 4 4 X : 4 X 4 4 : x + x + x, x + x + 5x, x + 5x + x ; : 5 5 x x x, x x x, x + x 5x x x x 5 5 x x x x, x, x
6 : 5 x x x x x x 5 5 x 5, x, x : x y + y + y, x y + y + 5y, x y + y + y, x, x, x y, y, y :, y, y, y : x x x 5 y y y, y y y 5 x x x 7 4 9 6 7 4 y y y y 7x 4x + 9x, y 6x + x 7x, y x + x 4x D 5 c c c c 7 9 5 4, y D x x 5 x x 5 x + x 5 7x 4x + 9x ; y 6x + x 7x, y x + x 4x 4 A, A, A 5A
7 : A A 5A AA 5AA AB A B AA 5AA λa λ A E 5 A E E 5 E A E E ka k n A 8 A 5A 6 5 A : AB A + B, AB A + B, B A EB A 6 A : B A E A, AB + E A + B B AB + E A + B AB B A E A E B A E A + E, A E, A E B A + E 7 A diag,,, A BA BA 8E B
8 : A diag,, A, A A BA BA 8E A B B 8A A A B AB 8E A B AB 8E A A + E B 4E, A + E diag,,, A + E diag,,, B 4 A + E diag, 4, 8 A A diag,,, 8, ABA BA + E B : ABA BA + E AB B + A A A B A B + A E A A E A B A E A A n, A 8, A 8, A E A B 6E E A E A 6,, 6 B 6 E A 6 6 6
9 4 9 P AP Λ, P : P AP Λ A P ΛP, Λ, A A P Λ P P, P 4 A 4 AP P Λ, P 4, Λ 5 : A P ΛP, Λ, A k P Λ k P Λ diag,, 5, ϕa 5A 8 6A 9 + A P 5Λ 8 6Λ 9 + Λ P Λ 8 diag,, 5 8, Λ 9 diag,, 5 9, Λ diag,, 5, 5Λ 8 6Λ 9 + Λ diag,, 7 7 68 684, ϕa A8 5E 6A + A A k O k, E A E + A + A + + A k : E AE + A + A + + A k E A A A E O, A A + E, A A + E : A A E O A A E O AA E E [ ] A A E E A A E A + EA A + E 4E
A + EA E 4E A + E [ 4 ] A E E A + E E A 4, A A E O A + E A, A, A A : A A E A A A E, A A A, A A A, A A A A A A A A A A E A A A E E A A AA A, A A 4 n A A, : A, A ; A A n : A, A A, AA A E O A, A O, A O A A A AA A E : A A A E A n A A A n A A A A n 5 : A E E B O A O B A A B + B O A B
5 4 4 9 4 O 6 A 4, A 8 A 4 O 4 : A, A 4 A O A O A A O 8 A 8 O A 8 O A O A 8 A 8 A 8 A 8 A 8 A 8 8 4 8 4 A 4 6 A 4 O O A 4 5 4 5 4 O O 4 6 4 7 n A s B, O A ; B O : O An n C C B s s O C C 4 En O E O E s, C s n, C s s, C n n, C 4 n s O An n C C AC AC 4 B s s O C C 4 BC BC AC E n C A, AC 4 O C 4 O, A BC O C O, B BC E s C B
O A C C O B B O C C 4 A O A O ; C B : A O C B A A A A 4 E A O C B A A A A 4 AA AA CA + BA CA + BA 4 AA E A A, AA O A O, CA + BA O A B CA, CA + BA 4 E A 4 B O A B O A A A A 4 A B CA O B 8 : 5 8 ; 5 : 5 5 8 8 5 5 5 5 8 4 : A, B, C 4 A, B 4,
4 A B CA O B 4 4 4 8 5 6
:, 5, 6, 6, 7, 8 P75 : ; 4 4 5 4 ; 4 4 : 4 4 ; 4 7 7 4 8 7 4 4 + + 4 4 5 + + 4 4 7 5 4 5 4 4 4 4 4 7 4 8 7 4 4 4 4 8 8 6 6 5 4 4 8 8 9 7 7 8
A 5 + 8 4 4 7 4 + 4 4 4 5 5 4 4 4, P, P A : P64 4 4 A, E 4 5 5 4 5 6 8 5 6 +, 7 6 7 6 5 A, P, P A ; P Q, QA T : 7 6 5 + 4 A, E 4 4, 7 5 7 5 P 5 5 A T, E + 5 + 5 4 7
6 Q 5 4 7 4, : 5 ; : 5 4 / 7 9 7 6 7 6 4 4 9 5 4 9 5 4 4 + 4 4 4 6 4 4 6 4 6 + 6 + 4 6 6 4 + 6 6
7 4 6 6 4 5 A, B, X AX B; A, B, X XA B 4 : 4 A, B 6 6 9 5 9 5 6 6 9 5 + 5 4 4 A B c + 4c c c X A B 5 4 7 c c c c 4 4 4 4 5 c c C c 4 4 c 4c c 4 7 7 4 4 7 4 X BA 4 7 4
8 P65,, : AX B, X A B A, 6 A : AX X + A, AX X + A, X AX X A A EX A A E, A + + + X A E A 7,?? :,,,,,,, A, RA, 8 A B, A, B? : : A B a, A B, a
9, 5,, RA RB, a RB RB, a RB +, RB RA RB +, RA RB RB + 9 4,,,,,,,,,, :,,, 4, : ; : 4 4 8 7 ; 7 5 5 8 7 5 8 4 4 4 4 4 6 5 4 6 5 4 6 5 ; +,, 4, +,, ; 7, 8 7 4 8 4 7 5 7 5 5 8 4 6 4 5 4 5
4 + 5 4 5 ; 7 5 5 8 5 5 8 7, A, B m n, A B RA RB : P68 E O RA, A F, O O E O A O O E O, B F, O O E O B O O, A A B k k k, k, RA ; RA ; RA : k A k k k + k k k k k, k k, RA c c k k k k k k k k,
4 k, A, RA k, A, RA : A, RA, k k A k 6 k k k k k 6 k k 6k k + k k, k k, RA + 6 k k k k k : x + x + x x 4, x + x + x x 4, x + x + x x 4, x + 6x x x 4, x + x + x + x 4 ; 5x + x + x 5x 4 ; x + x x + 5x 4, x + 4x 5x + 7x 4, x + x + x 7x 4, x x + x x 4, 4 4x + x x + 6x 4, 4x + x x + 6x 4, x x + 4x 7x 4 ; 7x x + x + x 4 : : 4 4 4 + 4 4 4 x x x x 4 c 4 4 x 4 x 4, x x 4, x 4 x 4, x 4 x 4, c
4 : 6 4 5 5 5 4 4 x x + x 4, x x, x, x 4 x 4 x x x c + c, c, c x 4 : 5 4 7 7 4 5 4 6 7 4 7 4 6 4 7 4 7 7 4 4 7 4 4 9 9 4 7 9 4 7 9 9 5 4 7 4 7 + 4 4 7 4 7 4 7 5 5 x, x, x, x 4 4 : 4 5 7 4 5 7 + 4 6 4 7
x 4 x 4 4 4 5 7 7 7 7 9 9 7 7 x 7 x 7 x 4, x 9 7 x 7 x 4, x x, x x x x 4 c 4 : 4x + x x, x x + x, x + x 8; x + y z + w, 4x + y z + w, x + y z w ; 7 9 7 :, 4 8 + c 7 7 4, c, c x + y + z 4, x y + 4z 5, x + 8y z, 4x y + 9z 6; x + y z + w, 4 x y + z w 4, x + 4y z + 5w ; 8 4 6, RA, RB, : 4 4 4 5 + 4 5 8 4 4 9 6 4 5 4 5 4 7 7 4
44 x z, y z +, z z x y c +, c z : 4 x y + z +, y y, z z, w x y z c + c +, c, c w 4 : 4 + 4 4 5 7 6 7 7 7 5 9 5 5 9 7 7 5 7 x y z w c 7 5 7 + c 7 9 7 + x 7 z + 7 w + 6 7, y 5 7 z 9 7 w 5 7, z z, w w 6 7 5 7, c, c 5 x c + c 4
45 : x c c, x c + 4c,, x c, x 4 c x x x 4, x x + 4x 4, x x, x 4 x 4 { x x + x 4, x + x 4x 4 6 λ, ; ;? λx + x + x, x + λx + x λ, x + x + λx λ : A, A λ λ + λ c +c +c λ + λ λ + λ λ + λ λ + λ λ + λ, λ λ λ λ, λ λ, 4 B 4 4 4 6 + + 6 9 RA < RB, λ, B RA RB,
46,,, RA RB, B λ λ λ λ λ λ λ λ λ λ λ λ + λ λλ + λ + λ, λ + λ, λ, 7 x + x + x, x x + x λ, x + x x λ, λ? : λ B λ λ λ λ λ + + λ + + λ λ λ λ λ +, λλ +, λ, λ λ, x x x c + λ, x x x c + 8 λx + x x, x + 5 λx 4x, x 4x + 5 λx λ, λ,? : A, λ λ λ A 5 λ 4 + 5 λ 4 λ 5 λ 4 4 5 λ λ λ λ 4 +4 λ + 9 λ λ 4 λ 9 λ λ λ
47 λ λ, λ, 8 B 5 4 4 5 + 4 + 8 8 9 5 4 9 9 9 7 5 4 9 9 9 RA, RB, λ, B 4 4 4 4, x x c + c x +, c, c R 9 RA a b T, A ab T : A ab T 7 Rab T Ra Ra, RA Rab T RA, a, b T, a i, b j A a i b j A, RA,, RA RA P, Q, O A P Q P O O,, Q a P, b,, Q, P, Q,, a, b T A, AB C, Bx Cx : Cx ABx Bx, ABx Bx Cx, ABx, A,, Bx
48 A m n, AX E m RA m; : P77 6, AX E m RA RA, E m A m n, 5, RA m m RE m RA, E m RA, RA m
A : a, a, a ; B : b, b, b 4 4 B A, A B : B A, P84, A a, a, a A, B a, a, a, b, b, b 4 A, B 4 5 5 5 4 4 6 5 7 4 5 4 4 6 5 7 8 7 9 4 6 5 7 4 5, 4, RA RA, B,, B A 4 B 4 4, RB RA, A B A B, RA RB P85 A : a, a ; B : b, b, b, A B : P85 RA RB RA, B A, B, RA RA, B B + 49,
5 RB RA RB RA, B A B A B b a a, b a + a, b a + a, a b + b, a b b Ra, a, a, Ra, a, a 4, a a, a ; a 4 a, a, a : P9 7 Ra, a, a 4, a, a, a 4 a, a P89 5 Ra, a, a <, a, a, a P89 5 a a, a a 4 a, a, a a a, a, a 4 a, a Ra, a, a 4 a 4 a, a, a 4 :,, 4 : A ; 4 + +, 4, 7 7, RA, : A 4 + + 7 7, : + 4, B 4,
5 RB, 5 a? a a, a a, a : a, a, a Ra, a, a <, A, A a, a, a a a + a A a a a + a a + a a a, a a 6 a, a, a + b, a + b, b a, a : b k a + k a a + b, a + b, x, x b k a + k a, x a + b + x a + b [ x k + + x k ] a + [ x k + x k + ] a 4 a a, a, { x k + + x k, x k + x k + 4 x, x, 4, k + k k k + k + k + b k a + k a k a + k a, b ca + ca, c R 7 a, a, b, b, a + b, a + b? : a, a, b, b, 4 a + b, a + b 4, a, a, b, b, a + b, a + b 8 : a, a,, a m, a a,, a m
5 λ, λ,, λ m λ a + + λ m a m + λ b + + λ m b m, a,, a m, b,, b m λ, λ,, λ m, λ a + + λ m a m + λ b + + λ m b m, a,, a m, b,, b m 4 a,, a m, b,, b m, λ, λ,, λ m λ a + + λ m a m, λ b + + λ m b m : a e,,,,, a a a m, a, a,, a m, a a,, a m λ, λ,, λ m λ a + + λ m a m + λ b + + λ m b m, 4 λ a + b + + λ m a m + b m 44 a b e, a b e,, a m b m e m, e,, e m, 44, a,, a m, b,, b m λ, λ,, λ m, λ a + + λ m a m + λ b + + λ m b m, a + b, a + b,, a m + b m a a a m, b,, b m, a, a,, a m 4 a, T, a, T, b, T, b, 4 T, } λ a + λ a λ λ λ b + λ b λ 4 λ λ λ 9 b a + a, b a + a, b a + a 4, b 4 a 4 + a, b, b, b, b 4 : b b + b b 4, b, b, b, b 4 b a, b a + a,, b a + a + + a, a, a,, a, b, b,, b
5 : k b + k b + + k b, 45 k + + k a + k + + k a + + k i + + k a i + + k a 46 a, a,, a, k k k k + k + + k, k + + k, k, 45 k k k b, b,, b, P88 6 b, b,, b a, a,, a,, 47, b, b,, b Rb, b,, b Ra, a,, a b, b,, b a, a,, a ; a b, a b b,, a b b, a, a,, a b, b,, b a, a,, a b, b,, b a, a,, a,, b, b,, b B b, b,, b, Rb, b,, b Ra, a,, a B b, b,, b a, a + a,, a + a + + a c c a, a,, a, c c, Rb, b,, b Ra, a,, a, b, b,, b, :
54 9 a, a, a 4 ; 4 4 8 a T,,,, a T 4,, 5, 6, a T,, 4, 7 : a T a T a T 4 9 4 4 8 + 9 a, a, a, a, a a, a 4 8 9, : a a, a, a a a,,, a, a a, a a T a T a T 4 5 6 4 7 4 a T, a T, a T, a T, a T 9 9 8 9 9 8, 5 5 :, 5 7 4 75 94 5 75 94 54 4 ; 5 5 48 4 5 7 4 5 7 4 5 7 4 : 75 94 5 4 75 94 54 4, 4 5 48 5, 4 a, a, a a 4, 8 5 7 4 5 9 5 a, a, a a 4 7 5, a 4 8 5 a a + a 4 a, a, a a 4, 5 4 4 + 4 4 5 + 5 5 4 4,
55 a, a, a, a 4 a + a a, a 5 a + a a, b,,, a, b : 4 a, a, a, a 4, A a, a 4, A, a, a 4 A a, a a, a 4 x, y, a b 5 a x + y, 4 a, a,, a n n, n e, e,, e n, a, a,, a n : e, e,, e n a, a,, a n, Re, e,, e n Ra, a,, a n P85 Re, e,, e n n, Ra, a,, a n n, Ra, a,, a n n a, a,, a n a, a,, a n e, e,, e n,, Ra, a,, a n Re, e,, e n n, a, a,, a n 5 a, a,, a n n, : n : n a, a,, a n, n e, e,, e n a, a,, a n a, a,, a n a, a,, a n n b, a, a,, a n, b n + n P89 5, b a, a,, a n : a, a,, a n, n, R n, n 6 a, a,, a m, a, a k k m, a k a,, a k : a k a a, a, a a a, a, a, a, a, a, a
56, a, a,, a m 7 B: b,, b A: a,, a s b,, b a,, a s K, K s, A B K RK : B B b,, b, A a,, a s B AK 48 RB RAK RK 49 B RB, RK K s, RK min{, s} RK RK x b + x b + + x b 4 4 4 Bx 4 48 AKx 4 A: a,, a s, RA 4 : Kx 4 RK, 4 : x b, b,, b,,, P88 6 8 β α + α + + α n, β α + α + + α n, β n α + α + + α n α, α,, α n β, β,, β n : β, β,, β n α, α,, α n α, α,, α n β, β,, β n β + β + + β n n α + α + + α n, β + β + + β n /n α + α + + α n
57 α β + β + + β n /n β, α β + β + + β n /n β, α n β + β + + β n /n β n α, α,, α n β, β,, β n, α, α,, α n β, β,, β n :, 9 A x A x Ax A x, x, Ax, A x, P x, Ax, A x, B, AP P B; A : P x, Ax, A x, AP Ax, Ax, A x Ax, A x, A x x, Ax, A x A x Ax A x P P, x, Ax, A x, P B P AP P P A P BP,, A B : x 8x + x + x 4, x + 4x + 5x x 4, x + 8x + 6x x 4 nx + n x + x n + x n : 8 A 4 5 8 6 x x x + x 4, x + 5x + 4x x 4, 8x + 7x + 6x x 4 8 5 5 4 8 4 8 8 4 4
58 + 4 4 4 4 4 4 { x 4x, x 4 x + 4 x 4, x x x x 4 4 c 4 + c 4 4 6 ξ 4, ξ 4, ξ 4, ξ 4 A 5 4 9 4 7 + 8 9 9 4 9 7 9 8 7 6 9 { x 9 x + 9 x 4, x 4 9 x + 7 9 x 4 x x x x 4 c 9 4 9 + c 9 7 9 ξ 9 4 9, ξ, ξ 4 9 9 7 9 x n nx n x x n, ξ 7 9 x x, x x, x n x n, x n nx n x x n ξ, ξ,, ξ n n n +
59 A 9 5 8, 4 B, AB O, RB : RB, B x x x x 4 AB 9 5 8 x x x x 4, 8 8 x x x x 4 9 5, x x x x 4 5, B 5, 5 B AB O, O, B B x x, x x 4 x x x x 4 x 5 x 6 x 7 x 8
6, ξ,,, T, ξ,,, T : x x x x 4 k + k, k, k R x k, x k + k, x k + k, x 4 k k, k { x x + x 4, x x + x 4 I : { x + x, x x 4 ; II : { x x + x, x x + x 4 : I II ; I II : { x x, I x 4 x ; x x, x x, x x, x 4 x ; I ξ, ξ II { x x x, x 4 x + x ; x x x, x x, x x, x 4 x + x ; II ξ, ξ
6 I II x + x, x x 4, x x + x, x x + x 4 4 + 4 +, x x, x x, x x, x 4 x ; I II x c, c R 4 n A A A, E n, RA + RA E n : 6 8 : A A, AA E O, 8P7, RA + RA E n 6P7, RA + RA E RA + RE A RA + E A RE n RA + RA E n RA E RE A, R A RA, RkA RA, k 5 A n n, A A, n, RA n, RA, RA n,, RA n : RA n A n, A A, RA n RA n A n, A, RA 44 RA n A, AA A E O
6 8 RA n, 44 45 RA + RA n RA 45 RA RA n A n, A O RA 6 : x + x 5, x 5x + x x 4, x + x + x + x 4, 5x + x + 6x x 4, 5x + x + x + x 4 ; x + 4x + x + x 4 6 : 5 5 5 B 9 5 5 9 4 5 8 B 4 8 η, ξ 5 5 5 6 4 6 4 4 7 8 9 5 7 + 5 7 7 η, ξ 9 7, ξ 7, η, η, η η 4, η + η 5 4
6 : Ax b A, 4, n 4, Ax η, η, η Ax b, η η, η η Ax, η η +η η Ax, Ax, η η + η η η η + η 4 5 6 Ax Ax b : x c 4 5 + 6 4 5, c R 8 A : a α b A ;, a b A, ; 5, a b A,, 4, b : x a + x a + x a b, β, α, β αx x x, x + x + x β, x + 5x + 4x 46 46 A a, a, a, α α + 4 A c c 5 4 5 4 α + 4, A, α 4, b A, α 4, A, b 4 β 5 4 + 5 + β β 5β β + β β,, α 4 β, 46, b A ;
64 α 4 β, 46, β A, b + β β, 46 x x, x x, x x c, x c, x, α 4 β, b A,, b ca c + a + a, c R 9 a a a a, b b b b, c c c c, l : a x + b y + c, l : a x + b y + c, a i + b i l : a x + b y + c, i,, : a, b, a, b, c : a x + b y + c, a x + b y + c, a i + b i, i,, a x + b y + c 47 47 xa + yb c 48 48 Ra, b Ra, b, c 49 Ra, b, c Ra, b, c, a, b, c a, b, c 49 Ra, b Ra, b, c a, b, a, b, c A a, a, a, a 4, a, a, a 4, a a a b a + a + a + a 4, Ax b : x x, x, x, x 4 T, Ax b a x + a x + a x + a 4 x 4 b b a + a + a + a 4, a a a, x + x a + x + x a + x 4 a 4
65 a, a, a 4, x + x, x + x, x 4 4 4 x x +, x x, x 4 x x, x x +, x x, x 4 Ax b x x x x x 4 c +, c R RA, n 4, Ax a, a, a, a 4 a a + a, Ax,,, T b a + a + a + a 4 a, a, a, a 4 A,,,, T Ax b Ax b k +, k P a, a, a 4 A a, a, a, a 4 a, a, a 4 P B, b a + a + a + a 4 a + a 4 a, a, a 4 P β Ax b P Bx P β, P Bx β
66 P 4, RP, P y, Bx β Bx β, x x x x 4, x x x x 4 k +, k η Ax b, ξ,, ξ n, : η, ξ,, ξ n ; η, η + ξ,, η + ξ n : η, ξ,, ξ n ξ,, ξ n, η ξ,, ξ n, η Ax, η Ax b η, ξ,, ξ n η, ξ,, ξ n η, η + ξ,, η + ξ n, η, ξ,, ξ n, Rη, η + ξ,, η + ξ n Rη, ξ,, ξ n n +, η, η + ξ,, η + ξ n η,, η s Ax b s, k,, k s, k +k + +k s x k η + k η + + k s η s : η,, η s Ax b s Aη i b, i,, s Ak η + k η + + k s η s k Aη + k Aη + + k s Aη s bk + + k s b, Ax b, x k η + k η + + k s η s x k η + k η + + k s η s Ax b, η,, η n + n + n + x k η + k η + + k n + η n +, k + + k n +
67 : x Ax b η, η,, η n + Ax b Ax b η, η,, η n + η η, η η,, η n + η, 4 c j c j,, n + η, η η,, η n + η, η, η,, η n +, η, η η,, η n + η, η η, η η,, η n + η, Ax b Ax b x x k η η + k η η + + k n + η n + η + η, x k k k n + η + k η + k η + + k n + η n +, k k k k n +, k + k + k + + k n +, x k η + k η + + k n + η n + 4 V { x x, x,, x n T x,, x n R x + x + + x n }, V { x x, x,, x n T x,, x n R x + x + + x n } V, V?? : V : α V, β V, α + β V ; α V, λ R, λα V α V, β V, α α, α,, α n T, α + α + + α n, β β, β,, β n T, β + β + + β n α + β α + β, α + β,, α n + β n T, α + β + α + β + + α n + β n β + β + + β n + α + α + + α n α + β V 4 λ R, λα λα, λα,, λα n λα + λα + + λα n λα + α + + α n λ
68 λα V 4 4 4, V V, : α + β + α + β + + α n + β n β + β + + β n + α + α + + α n + α + β / V 5 : a,, T, a,, T, a,, T R : A a, a, a, A a, a, a RA, a, a, a a, a, a,, a, a, a, a, a, a R 6 a,,, T, a,,, T L, b,,, T, b,,, T L, L L : a, a b, b a b + b, a b + b ; b a + a, b a a P, L L 7 a,, T, a,, T, a,, T R, v 5,, 7 T, v 9, 8, T : A a, a, a A 6, A, a, a, a, R v k a + k a + k a, v λ a + λ a + λ a k, k, k λ, λ, λ, Ax v Ax v 5 9 5 9 A, v, v 8 + 4 5 7 7 7
69 4 5 9 5 9 4 5 7 4 5 7 4 8 8 9 9 Ax v Ax v, k, k, k, λ, λ, λ v a + a a, v a a a 8 R a, a, a a, a, a b, b, b b, b :, a, a, a b, b, b A a, a, a, B b, b, b A, B 4 4 + 4 4 P A B, 4, b 4 4 4, 4 P A B 4
4 a, b, c a, b λa + c, λ c : c x, y, z T, x z, 4 λ + x, y, λ + z λ, c,, T : a, a, a 4 ; 9 a, a, a :, : b a, b a [b, a ] [b, b ] b, b a [b, a ] [b, b ] b [b, a ] [b, b ] b b, b, b b a, b a [b, a ] [b, b ] b, 7
7 b a [b, a ] [b, b ] b [b, a ] [b, b ] b 5 4 b, b, b 5 5 5 4 5? ; 9 8 9 4 9 8 9 9 4 9 4 9 4 7 9 9 :,,, 4 x n, x T x, H E xx T, H : A + B T A T + B T, H H H H T E xx T T E T xx T T E x T T x T E xx T H H T H E xx T E xx T E xx T xx T + 4xx T xx T x T x E 5 A B, AB : A, B, A A T, B B T AB AB T AB B T A T AB B A AB E 6 : 5 ; 6 ;
7 : A λe λ 5 λ λ c λ+c λ λ 5 λ 5λ 7 λ +, A λ λ λ λ λ λ, A + Ex, A + E 5 + + 5, p kp k λ λ λ λ A λe λ λλ + λ 9, 6 λ A λ, λ, λ 9 λ, Ax, A 6 p +, k p k λ λ, A + Ex, A + E p 7,, k p k λ λ 9, A 9Ex, 8 5 5 A 9E 8 + 5 5 + p, k p k λ 9,,
7 λ A λe λ λ λ λ λ λ + +4 λ λ λ λ λ λ λ λ + λ, λ λ, λ λ 4 λ λ, A + Ex A + E, p, p λ λ k p + k p k, k λ λ 4, A Ex A + E, p, p 4 λ λ 4 k p + k 4 p 4 k, k 4 7 A n, A T A
74 : A T A, A T A A T λe A λe T A λe 8 n A, B RA + RB < n, A B, : RA + RB < n, RA < n, RA < n A A E A, B A B A B λ A B λ p Ap p, Bp p Ax Bx A x B A B R A B RA + RB < n 9 A A + E O, A : λ A, λ λ + A A + E p A A + Ep λ λ + p A A + E O, λ λ + p p, λ λ + λ A : A A + E O, A EA E O A EA E A E A E A E A E, A A, A, A P 8
75 A, A, λ A : λ A λe, A + E A + E A + A T A A E + A T A A T + E A A + E T A + E, A + E, A + E λ A λ m A m n B n m, λ n BA : p A m n B n m λ, ABp λp 5 B BABp Bλp, BABp λbp Bp, Bp, 5 ABp ABp ; λ, p, λp λ n BA : A,,, A 5A + 7A : P 9 λ A, ϕa A 5A +7A, ϕλ λ 5λ +7λ ϕa ϕ, ϕ, ϕ, ϕa,,, A 5A + 7A 8 A,,, A + A + E : A A A, A λ A, ϕa A + A + E ϕλ A λ + λ + A + A + E ϕ, ϕ 5, ϕ 5, A + A + E 5 5 5 4 A, B n, A, AB BA : A AB BA 5 A x 4 5 A ABA A ABA BA,, x
76 : : 4 P, n A A n λ A λe λ x 4 5 λ λ λ 4 5 λ λ λ 6, λ 6, λ λ A, A,, A, λ λ, A Ex P97 7, n RA E, RA E A E x 4 4 x x,, x, A 6 p A 5 a b a, b p ; A? : p λ, Ap λp, Ap 5 a + a λ, b + b λ, a, b A λe λ 5 λ λ λ +, λ λ λ A, λ λ λ, A + Ex n RA + E A + E O, RA + E, n RA + E,, A + Ex A
77 7 A 4 4 4, A : A λ 4 A λe λ 4 4 λ λλ 5λ + 5, A λ, λ 5, λ 5 λ, A Ex 4 A E 4 4 4, λ p,, T λ 5, A 5Ex 4 4 A 5E 8 4 4, λ 5 p,, T λ 5, A 5Ex 6 4 A 5E 4 4 8, λ 5 p,, T P p, p, p, Λ diag, 5, 5, Ap, p, p p, p, p diag, 5, 5, AP ΛP, A P ΛP A P Λ P 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 5 5,
78 a d b c a d b c a a + cd b c, d c a, a c a b c a n c n a n b n c n a c a b c c a c a b a c a b c a n c n a n b n c n A 4 5 5 5 5 5 5 5 5 5 5 5 5,, A, A5 A,,, A 5,,,,,,,,, A 5 4,, 4,, 8A 8 8 8 8 8 8 8 8 8 A A,
79 A 5 4 A 8 8 8 8 8 8 8 8 8 a a a A b b b, A6 c c c a : A b,,, c a a a A 6 b,, b,, b,, c } c {{ c } 6 A a a a b,, b,, b,, c c c }{{} 5 a+b+c a a a a + b + c 5 b b b c c c 8, p, q, n x n y n x n + y n xn+ y n+ A xn y n ;, : x n+ px n + qy n, y n+ px n + qy n x y 5, 5 xn+ y n+ xn y n p q p q xn y n, p q A p q x y 5, 5 xn y n A xn xn y n y n A n x A n 5 5, y,
8 A n A λe p λ p q q λ λ λ p q, A λ, λ p q λ, A Ex A E p q p q q λ ξ p λ p q, A p qe x A p qe q q p p p q λ p q ξ P ξ, ξ, P, AP P diag, p q A P diag, p q P, xn y n A n x P P x y p q n y q q p p q n p + q p + q p p q n,, 9, : ; 5 4 4 5 : λ A λe λ λλ 4λ +, λ A λ, λ, λ 4 λ, 4 x x x, p x x x k
8 λ, x x x, p λ 4, x x x k 4 x x x, x x k x p p, p, p P, A P AP 4 A λe λ 5 λ 4 4 5 λ λ λ, λ λ, λ λ λ, 4 4 4 4 x x x, x x x k + k
8 ξ,, T, ξ,, T ξ, ξ, η ξ, η ξ [η, ξ ] [η, η ] η 4 /5 5 4/5 p η η 5, p 5 4 5 λ, 8 5 4 4 5 x x x, p A A P AP Λ 4 x 4 x x x p, p, p k P AP Λ 5 5 5 4 5 5 5 5 5 4 y, x, y; P, : A Λ, 5, 4, y A A 5E, A + 4E A + 4E, 5 4 5 4 4 A + 4E x + 4 x + 4 c +c 4 x + 4 9x 4, 4 5 9 9 9 x 4 y A λ λ λ 5 4 y, 4 A 4 4 4 4 5 5 c +c 4 4 4 5,
8 y 5 P λ λ 5, A 5Ex 4 4 A 5E 4 4, ξ,, T, ξ,, 5 T p,, T, p 4 5 5, 5 5, T λ 4, A + 4Ex 5 4 A + 4E 8, 4 5 ξ,, T, p,, T P, P p, p, p 5 5 4 5 5 5 P AP diag5, 4, 5 P p, p, p, Λ 5, 4, 5 A 5Ex, ξ,, T, ξ, 4, T, p,, T, p, 4, T P p, p, p 4 x, y A Λ, 5, 4, y A λ + λ + λ a + a + a A λ λ λ, λ + λ + λ + x +, λ λ λ A 5
84 A 4 x 4 4 x 5 5 c +c 4 4 x 5 5x 4, 5 + y + x, y 5x 4 x 4, y 5 A λ, λ, λ ; p, p, p, A : P p, p, p, Λ diagλ, λ, λ, AP P Λ, A P ΛP c c 4 4 c c 4 5 4 4 c c 4 5 4 4 4 5 4 4 A P ΛP 4 5 4 4 A A λ, λ, λ ; λ, λ p, p : λ p x, y, z T A, λ λ λ, p, p, p x + y + z, x + y z 5 A +,
85 5 x, y, z T k,, T p,, T, A, Q, Q T AQ Q AQ diag,, p, p, p,, / / / Q / / / / / / A Q diag,, Q T 9 A λ 6, λ λ, λ 6 p,, T, A : λ, λ p, p 6, p, p p x, y, z T p, x + y + z A,, T,,, T p,, T, p,, T Ap, p, p 6p, p, p, A 6p, p, p p, p, p 6 6 6, 6 6 6 c + c c c 6 9 c c c 4 4 4 4, A p, p, p diag6,, p, p, p 4 4 4
86 4 a a, a,, a n T, a, A aa T, λ A n ; A n : A, A Λ diagλ, λ,, λ n, λ, λ,, λ n A 9, RA, RΛ, Λ, λ A n n n A aa T a i ; : A n a i, λ A n, n a, a i, i A i n a i i n a i A i a λ n, Ax a a a a a n a a a n a a a n a a a a a n a a a a a a n i a i A, i,, a n a a n a a n a n a a n a a n i λ n n a a, a a,, a n a n b λ a i, A aa T, i Aa aa T a aa T a a n n a i i i a i a, a a, a,, a n T λ n a i i, A n : a a n a a, a a, a a,, a n a 5 A, ϕa A 5A 9 ;
A 87, ϕa A 6A 9 + 5A 8 : A A λe λ λ λ 4 λ 5λ, A λ 5, λ λ 5, A λe A 5E, ξ, T λ, A λe A E, ξ, T Aξ, ξ ξ, ξ diag5,, P ξ, ξ, Λ diag5,, A P ΛP 5 A 5A 9 P Λ P 5P Λ 9 P 5 P P 5 4,, A λ A λe λ c +c +c 5 λ λ λ λ λ 5 λλ λ + λ A λ 5, λ, λ λ 5, A 5E 4 + + 4 4, ξ,, T ; λ, A E,
88 ξ,, T ; λ, A + E, ξ,, T ξ, ξ, ξ,,, p,, T, p,, T, p 6,, T P p, p, p 6 6 6, Ap, p, p p, p, p diag5,,, Λ diag5,,, A P ΛP, A k P Λ k P A 6A 9 + 5A 8 P Λ 6Λ 9 + 5Λ 8 P 6 6 6 6 6 4 6 6 6 6 6 6 6 4 4 4 4 8 6 : f x + 4xy + 4y + xz + z + 4yz; f x + y 7z xy 4xz 4yz; f x + x + x + x 4 x x + 4x x x x 4 + 6x x 4x x 4 x : f x, y, z 4 y z x f x, y, z y 7 z f x, x, x, x 4 x x x x 4 7 : fx x T x; fx x T 4 5 6 x 7 8 9 : a ij a ji,, a ij a ji :
89 A 5 A 5 7 5 7 9 8 : f x + x + x + 4x x ; f x + x + x + x 4 + x x x x 4 x x + x x 4 : f A λ A λe λ λ5 λ λ, λ A λ, λ 5, λ λ, A Ex, A E ξ, p ξ λ 5, A 5Ex, A 5E, p λ, A Ex, A E, ξ, p, x y x y, x y
9 f A f y + 5y + y λ A λe λ c +c +c +c 4 λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ + λ λ λ + λ λ + λ λ, λ A λ, λ, λ λ 4 λ, A + E + 4 + 4 + + + 4 4 + ξ,,, T, p,,,, T, λ, A E + 4 + + 4 + 4, ξ,,, T, p,,,, T
9 λ λ 4, A E 4 + +, T, : ξ,,, T, ξ 4,,, T, p,,, p4 x x x x 4 9 f y + y + y + y 4 y y y y 4 x + 5y + 5z + 4xy 4xz yz : A 5 5 5 5 T,,, A λe λ 5 λ 5 5 5 λ λ 5 λ 5 λ λ λ 4 λ 5 λ λ λ λ, A λ, λ, λ λ, A λe A 5 5 + 5 5 5 5 λ ξ,, T p,, T, λ, A E 5 5 + 5 + 4, λ ξ 4,, T p 4,, T
9 λ, 8 A E 6 5 5 6 + 4 6 5 + 6 5 + 5, λ ξ,, T p,, T P p, p, p 4 x, y, z T P u, v, w T, x + 5y + 5z + 4xy 4xz yz v + w v + w : f x T Ax x A : x P y, f x T Ax P y T AP y y T P T AP y y T Λy λ y + λ y + + λ n y n, λ, λ,, λ n A, x x T x P y T P y y T P T P y y T P P y y T y y,, x, y + y + + y n y λ i max{λ, λ,, λ n }, f λ y + λ y + + λ n y n λ i y + λ i y + + λ i y n λ i y + y + + y n λ i, y e i,,,,,, T, f λ i max f max{λ, λ,, λ n } x, : fx, x, x x + x + 5x + x x 4x x ; fx, x, x x + x + x x + x x ; fx, x, x x + x + 4x + x x x x ; : f x + x + 5x + x x 4x x x + x x + x + x + 4x x x + x x + x + x x, y x + x x, y x + x, y x, x y y + y, x y y, x y,
9 f f y + y y, C f x + x + x x + x x x + x + x + x x x + x + x + x x, y x + x, y x + x, y x, x y y + y, x y, x y y, f f y + y y, C f x + x + 4x + x x x x x + x x + x + x + x x x + x x + x + x + x, y x + x x, y x + x, y x, x y y, x y y + y, x y, f f y + y + y, C fx, x, x x + x + 5x + ax x x x + 4x x, a : A a a 5, a a >, a a 5 >
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