6 6.1 6.2 6.3 6.4 6.5 6.6 6.7

Vector SpacesLinear Spaces. . . ..

6.1

A+B=B+A(A+B)+C= A+( B+C) OA=AA+(-A)=Oa(A+B)= aA+Ab(a+b)B=a B +Bb(ab)A=a(b)A8. 1AA

2 RV3.R8.x,y,z . . 8.

1FV.VV(c1) V()u,vV, u+vV.(c2) FV ()Fa Vv, avV.(a1) u+v= v +uuvV.(a2) u+(v+w)= (u+v)+w, uvwV.(a3) Vo, v+o= v Vv.(a4) Vv, Vu u+v= 0. uv.

(m4) 1u= u uV.

4 FF[x]F.

(a2) [f(x)+g(x)]+h(x)= f(x)+ [g(x) +h(x) ], (a3) 0. (a4) f(x)- f(x).

5 C[a,b][a,b]R.3.6 1FF.2RQRC

7 R, R+()

3.4.

51082.

.

1 0.2 v- v.

6.2 1.2.3.

1VFWV . 1WWWV. 2WFaaWW .

2WFV.W V . 3WFV.W V WV . VFV

V{0}VV VVVV

V2V2V3V3

F [x]nF [x] [a,b]C [a,b]

1 A0 = 0

4WWVa,bF,W a+bW

1W1W2VW1W2V.2 {Wi }V. V.3W1W2

W1+W2V,W1W2 .

6.36.3.1 6.3.2 6.3.3 6.3.4 1 23

6.3.1 1

6.3.2 2

1 1=1,2,32=2,4,63=3,5,-42 1=1,-2,32=2,1,03=1,-7,93 F [x] n ,

6.3.1 6.3.2 6.3.3

6.3.4 6.3.5

6.3.3

6.3.6 (6.3.7

6.3.4

5F36.3.8 .

6.4 6.4.1 6.4.26.4.3 6.4.4 12

6.4.1

1

2Fn.

6.4.1

6.4.2 1 VV

3 4

dimnnmnmn

.. 5 x...3 nn

..

6.4.3 .. dimdimdimdim6.4.4 .. 6 VWW . V W W

6.4.7 n VW , WW , dimV = dimW + dimW.

6.5 6.5.1 6.5.2 6.5.3 1..2..

6.5.1 1

1 2 3

.

6.5.2 2

4

6.5.3 6. 5. 2

(4)

5 ,6

6.6 6.6.1 6.6.2 6.6.3 1..2.. .

6.6.1 1 if VW6.6.2

2. f VW

6.6.3 1 2 .3

67 6.7.16.7.2 123 .

6.7.1 Fmn

iPAA iiAQA

4.

6.7.2F1 F1

A2 2

3

3 1

,

.

4 F4 AX = 0 AX = B44