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1 R 3 R n C n V??,?? k, l K x, y, z K n, i x + y + z x + y + z iv x V, x + x o x V v kx + y kx + ky vi k + lx kx + lx vii klx klx viii x x ii x + y y + x, V iii o K n, x K n, x + o x iv x K n, x + x o x K n v kx + y kx + ky vi k + lx kx + lx vii klx klx viii x x 2 V x, y V x + y V,R n,c n 2 V 2 {o}, o + o o, ko o, V 2 3 V 3 Mm, n 4 A Mm, n V 4 { Ax o } {x K n Ax o} 5 b o, k K, x V kx V V 5 { Ax b } {x K n Ax b}, k, l K x, y, z V, i x + y + z x + y + z ii x + y y + x iii o V, x V, x + o x 6 P {fx fx }, f + gx fx + gx kfx kfx, P

2 2 7 V 7 {fx fx 3 } 8 P 3 {fx fx 3 } 9 V 9 {fx fx f x 2fx } V {fx fx f x 2fx + } V {{a n } {a n } a n+2 a n+ + a n n } 2 V 2 {{a n } {a n } a n+2 a n+ a n n } 3 V i V ii x V x iii x V x, x x iv x, y, z V, x + y z x z + y v x V, x o 2 4 V W V, W V 3 V 4 K n 4 V 7 V 6 5 W V W, a K x, y W, x + y W ax W 6 W V W, a, b K x, y W, ax + by W 5 W 5 {x, y R 2 y ax} R 2 6 b, W 6 {x, y R 2 y ax + b} R 2 7 W,W V, W W V vi x V, x x vii k K, ko o viii k K x V, kx o k x o W,W V, W W V 8 W,W V, W W W + W 9 W + W {x + y x W, y W }

3 3 7 R 2 W {x, y R 2 y px} W {x, y R 2 y qx}, p q i W W V ii W W V iii W + W V 3 V {x, x 2,, x n }, k x + k 2 x k n x n k, k 2,, k n K V x, x 2,, x n,, x, x 2,, x n {k x + k 2 x k n x n k, k 2,, k n K} {x, x 2,, x n } 2 V {x, x 2,, x n }, x, x 2,, x n V 3 V {x, x 2,, x n }, k x + k 2 x k n x n o k k 2 k n, {x, x 2,, x n },, R 3 4,, R 3 4,, P 2 { 2 + 4t + 4t 2, 3 + 3t 2, 8 + 4t + t 2} 2 P 2 { 2 + 4t + 4t 2, 3 + 3t 2, 8 + 4t + 4t 2} 4 {x, x 2,, x n } x i n 5 V {e, e 2,, e n } 2, V i {e, e 2,, e n } ii V 22 R 3,, R 3 4,, R 3 4,, R 3 4, 4 3

4 R 3 4,, 4, V {e, e 2,, e n } V, 7 V {o} i dim W W {o} 2 ii dim W W { }, W iii dim W 2 W 2 { } 8 V,, W 2 9 V, dim V 2 V {e, e 2,, e n }, V, V,, V, 2 dim V n V {x, x 2,, x n }, 22 W V, dim W dim V, dim W dim V, W V 27 dim R 3, W R 3, dim W, dim W,,, iv dim W 3 W 3 28 P 3,, dim P 3 29 V,, dim V 23 W, W 2 V, dimw +W 2 dim W + dim W 2 dimw W 2 24 V W +W V z x W, y2 W, z x + y, V W W, V W W 25 V W + W 3 i V W W

5 5 ii W W {o} iii dimw + W dim W + dim W R 4 W W ,, W W 2, X,Y X x, Y y, i X ii Y X, 27 i X ii f x X fx, x iii X X, fx {fx Y x X } X iv fx v Y Y, f Y {x X fx Y } Y 3 f 3 : R R R x, R x 2 f 3 : x x 2, f 3 2 f 3 R f 3 { 2 x < 3} f3 { < y 2}

6 6 28 f : x x f : X X, I X I 29 f : X Y, g : Y Z, g f : X Z g f : x gfx, f g ii fx Y, f iii f, f 32 f 32 : x x 2, i f 32 : R R, f 32 g f, f g, g f f g 3 X {, 2, 3, 4}, Y {,,, } f 3 : X Y f 3 f 3 2 f 3 3 f 3 4, X {, 2}, Y {, }, f 3 X f 3 X f 3 f 3X f 3 Y f 3 f 3 Y f f I X, f f I Y 3 f : X Y ii f 32 : R [,, f 32 iii f 32 : [, R, f 32 iv f 32 : [, [,, f 32 3 f : X Y, g : Y Z, g f : X Z 32 f : X Y, g : Y Z, i g f, f ii g f, g 33 f : X Y y Y, fx y x X, y f, f : y x f 34 f : X Y g f I X f g I Y g : Y X, g f 35 f : X Y g f I X f g I Y g : Y X, g f 36 f : X Y i f : Y X ii f f I X iii f f I Y i fa fb a b, f iv f f

7 7 22 i f Imf fv V 37 V,V f : V V x, y V,k K, i fx + y fx + fy ii fkx kfx, 38 f : V V x, y V,a, b K, fax + by afx + bfy 33 f 33 : R 2 R 2 i f 33 : x x y,, ii f 33 : x x y x + y,, iii f 33 : x x y,, iv f 33 : x x 3 y y 3,, 34 A Mm, n, f 34 : K n K m f 34 : x Ax, 39 f : V V, ii f Kerf f {o} V 4 f : V V, i f Imf V ii f Kerf {o} iii dim V dim Imf + dim Kerf x 35 f 35 : R 3 R 2 x f 35 : y, z Imf 35 { }, dim Imf 35 Kerf 35 { }, dim Kerf P n {t n } i f 36 : P 3 P 2 f 36 : xt dxt/dt, f 36, Imf 36 { }, dim Imf 36 Kerf 36 { }, dim Kerf 36 ii g 36 : P 2 P 3 g 36 : xt t xsds, g 36, Img 36 { }, dim Img 36 Kerg 36 { }, dim Kerg V, V f : V V, V V, V V, f, V V, f

8 8 37 I : V V I : x x, I 42 f : V V, g f I g : V V, f, g f 43 f : V V f 44 f : V V V {e,, e n }, {fe,, fe n } V V V dim V dim V,,,, M2, 2, g 38 : 45 V {e,, e n } f : V K n, f f : k e + + k n e n dim V dim V < V V k k n 38 M2, 2,,,,, dim M2, 2,, M2, 2, f 38 :, 39 P 2,,,,, dim P 2,, P 2, f 39 :,,, P 2, 2 g 39 : n V K V i V ii {e,, e n } V, V f,, f n f i e j δ ij, i, j, 2,, n

9 9, V x c e + + c ne n, c,, c n K, f i x c i, i, 2,, n f i V, V iii V V 3 m V n V {e,, e m } {e,, e n} f : V V, fe,, fe m V, n fe i a ji e j, j i, 2,, m 46 A a ij {e,, e m } {e,, e n} f 47 V x u x + +u m x m f fx v x + +v n x n, v A u V V v n u m 48 m V n V Lm, n, Lm, n Mm, n 49 m V n V f, A, dimimf ranka x 4 f 4 : R 3 R 2 2x + 7y + z f 4 : y x + 3y + 2z z R 3,,,, R 2,,

10 , f 4 f 4 f 4, f 4 A 4 A 4, R 3 2,, f 4 3 f 4 f 4 3, , , R , f 4 B 4 B V 2 {x,, x n } {y,, y n } y i n p ji x j j i, 2,, n,, n P p ij, V {x,, x n } P p ij, {y,, y n } V 5 P 52 V x u x + + u n x n v y + + v n y n, P v v n 53 m V n V f, {x,, x m } {x,, x n}, f A, {y,, y m } {y,, y n} P,Q, {y,, y m } {y,, y n}, f u u n B B Q AP ,

11 , P ,, Q + +,,, 42 f 42 : P 2 P 2 f 42 : xt dxt dt P 2 {, t, t 2 }, f 42 + t + t 2, f 42 t + t + t 2, f 42 t 2 + t + t 2,, f 42 A 42 Q A 4 P 54 V V, B 4, P 2, {,, }, f , f , f ,, f 42 B V f, 5 i f ii f P + t + t 2, + t + t 2, iii f iv f v f V V, P + t + t 2,, P, 56 n V f, {x,, x n }, f A, {y,, y n }, f B {x,, x n } {y,, y n } P, B P AP P A 42 P B 42

12 2 3 R V P 4 {t 4 }, i dimv, V ii V xt, V d2 xt f : V V dt 2 iii i, f iv Kerf Imf v V R dimv vi t V 2 x, y, x, y C, 4, x, y,, V i x, y, z V, x + z, y x, y + z, y ii x, y V k K, kx, y kx, y iii x, y V, x, y y, x iv x V, x, x, x, x x o 43 R n x x y y, x, y x y + x n + x n y n 44 C n x x x n + x n y n 45 C n x x y y y n y y n y, x, y x y +, x, y x y + x n + x n y n 46 R 2 x x x 2 y x y 2 + x 2 y + 2x 2 y 2 y n y y 2, x, y 3x y +

13 3 4 R 2 x y x y, x, y ax x 2 y y + bx y cx 2y + dx 2y 2 a, b, c, d 47 P n xt, yt, x, y xtytdt 58 i x, y, z V, x, y + z x, y + x, z ii x, y V k K, x, ky kx, y iii x V, x, y y o iv x V, x, y x, z y z 59 V x, x x, x x 6 V, x, y V,k K, i kx k x ii x, y x y Schwartz iii x + y x + y 6 V x, y, x, y, x y, x y 48 R 2 43, V W, W {x V y W x, y }, W V 63 W W 64 V W W, V W W V, f : V K, x V, fx x, y y V 66 V, f : V V, y V, fx, y x, y, x V y V 67 y V, y V f, f 68 f f i f ii x, y V, fx, y x, f y iii f f iv f g g f 69 n A, A τ A A A 49, A 49 i 2 + 3i

14 4 7 A n A i x, y K n, Ax, y x, A y ii A A iii AB B A 7 V, f : V V V f Af, Af Af 72 V, f : V V i f f, f ii f f, f 73 A n i A A, A ii A A, A 5 A 5 5 A i / 2 i/ 2 / 2 5i i f, 6 a x, y V, fx, y x, fy b V f A, A a x, y V, fx, fy x, y b x V, fx x c f V d V f A, A 75 5 i A ii x, y K n, Ax, Ay x, y iii x K n, Ax x iv A K n v A K n V, f : V V, x V x o λ C, fx λx, λ f, x f λ 77 x f λ, αx f λ 78 A n, x C n x o λ C, Ax λax, λ A, x A λ ii f,

15 5 79 f A,, f A 8 n A, λ n deta λi A 8 n A a ij, tra n k a kk trace n A a ij λ n, λ n, 82 λ A λ deta λi 52 A 52 cos θ sin θ sin θ cos θ,,, 83 A,B, A B 84 λ A, W λ {x x λ } {o} λ 85 W λ C n 53 A 52, W { }, W { } 86 λ, λ 2 A λ λ 2, W λ x W λ 2 x 2 54 A 52, W W, 87 i ii V n f : V V V 89 n A P P AP n x,, x n P, P x x n 2 55 A 55 A 55 2 deta 55 λi, A 55, x, A 55 Ix o, x

16 6 y, A 55 Iy o, y x y, P, P A 55 P 56 A deta 56 λi, A 56 A 56, A 55 x, A 56 Ix o, x, A A 57 deta 57 λi A 57 z, A 57 Iz o, z x,y,z, P 58 A 58 A deta 58 λi 2 4, A 58, A 58, P A 57 P x, A 58 Ix o, x y, A 58 Iy o, y,,,, P, A 57,, x, A 57 Ix o, x y, A 57 Iy o, y, P A 58 P A 58

17 n A, P, P AP 3 59 A 59 A 59 deta 59 λi, A 59 x, A 59 Ix o,, x, x,, P,, A 59, P A 59 P 5 A P AP P 9 A A A AA, 6 i ii 92 λ, λ 2 A λ λ 2, W λ x W λ 2 x 2 93 n A, 3 i A ii P P AP iii A 6 A 55 P, Q 62 A A 62 deta 62 λi, A 62,, x y z, P A 55 P, Q A 55 Q A 62, x, A 62 Ix o, y, A 62 Iy o, z, A 62 Iz o, {x, y, z}, P

18 8, P A 62 P 63 A A 63 deta 63 λi, A 63, A 62 A 63, x, A 63 Ix o, x, y y, A 63 Iy o, {,, }, P, P A 63 P i A 64 deta 64 λi A 63 i 64 A 64 i i A 64,, A 64, x, A 64 Ix o, x, y y, A 64 Iy o, {,, }, P, P A 64 P 7 A A, H U A HU H U A U H 65 K C, A M,, A a re iθ a, H,U

i I II I II II IC IIC I II ii 5 8 5 3 7 8 iii I 3........................... 5......................... 7........................... 4........................ 8.3......................... 33.4...................

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