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K

K
 
 
 
 n  
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"
# $%
! 
&&&&&&&&&&&&&&
 
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α),,αn)
αv+ αv+ + αnvn=*
}
α=α==αn=*
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/+'-
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αv+αv+ …+αnvn*
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 $$
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$ 
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[
3
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=
 7" 8$$&9-1
$$'
(
vi
)
i1
$
0$
(
vi
)
i1
2
=vect
(
(
vi
)
i1
)
+'$  '
vect
(
(
vi
)
i1
)
2 

vect
(
(
vi
)
i∈ℕ
)
+$+ $
(
vi
)
i1
.'
$  '
 $ 
+'2$.6+2$ 
 $
(
vi
)
i1
+'  $+$
$':.
f
:
f

{
uEv, f
(
u+v
)
=f
(
u
)
+f
(
v
)
uE∀λ), f
(
λu
)
=λ f
(
u
)
5
0
(
 ( :
)
 :
$+ '
f0
(
 (:
)

b:
+
f
(
x
)
=b
+'
 
b:

x
+6
f
(
x
)
=*:
+';+6'
f
(
x
)
=*:
x) f
- +
f0
(
 (:
)

b:
6+
f
(
x
)
=b
-
b1 f
+
f
(
x
)
=b
2+ 
-
b1 f
+
f
(
x
)
=b
6'
x*
+
f
(
x*
)
=b
 
x*+) f
{
x*+xx) f
}
+'
x*+) f
&&$$
'
f
(
x
)
=f
(
x*
)
f
(
x
)
f
(
x*
)
=*:
f
(
xx*
)
=*:
.$'86
{
ax+by+cz=d
a' x +b' y+c' z=d '
(
abc
a' b' c'
)
(
x
y
z
)
=
(
d
d'
)
.$'
λ

{
φλ' ;
(
(
)
;
(
(
)
 ff 'λ f
0+
x∈ℝ

(
φλ
(
f
)
)
(
x
)
=x

f
+$$'
y' λ y=x

'
Ker f

1f
<+6
-
f0
(
( :
)
$
dim
(
)
=rg
(
f
)
+dim
(
) f
)
=<
1
(
f
)
Ker
(
f
)
>$?
/.&:@$'
dim
(
:
)
=dim
(
@
)
:@
}
:=@
A &@$$B. $ 
@
dim
(
@
)
'
n=dim
(
@
)
(
n
)
$ 
i
(n
i@
}
Vect
(
n
)
=@

/'
f0
(
 (:
)

b1 f

b1 f
A.
x

x

+
f
(
x
)
=b

f
(
x
)
=b
 +
f
(
x
)
=b+b

x+x+) f
'
f
(
x+x
)
=f
(
x
)
+f
(
x
)
=b+b

x+x
6
.'
 7" 8$$&9-1
 
$ '
f0
(
)
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λ)
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λ
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f
.
x

x*
+
f
(
x
)
x
+'
λ

f
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)
(
fλ 1
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{
*
}
0 
f
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f
'
-
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f
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λ))
(
fλ Id
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*
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$&C
λ
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f0
(
)
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λ
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f
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λ
&
λ
(
f
)
)
(
fλ Id
)
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λ
'
f0
(
)
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λ

f

&
λ
(
f
)

f
C

λ
;+$
D++$ '
E
h
 /?
p
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s
$ E
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λ)
=:@
/?:6C@
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v=v:+v@
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p
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v
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/
v=v:+v@
v::
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s
(
v
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=v:v@
1
;
v
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h
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v
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s
(
v
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s:=Idp@
-
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h
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λ
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λ
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h
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=
(
p
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(
p
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(
s
)
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(
s
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/+
=:@
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*:@
$+
+
:+@
/.&'&.

λ≠μ λ
(
f
)
μ
(
f
)
=
{
*
}
'
vλ
(
f
)
μ
(
f
)

f
(
v
)
=
/$$'$$C
 
 7" 8$$&9-1
'$
-
/k
'F$
k
C G
1'
k=


/

E'
k
$.-+
/k

-
(
vi
)
i
[
( k+
]
k+
+
( k+

viλ
(
f
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
ij
λiλ j
(
αi
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i
[
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)k+

f
(
αv+ …+ αk+vk+
)
=
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αv+ + αk+vk+=*

{
f
(
αv+ + αk+vk+
)
=
λk+
(
αv+ + αk+vk+
)
=

{
λαv+ + λk+αk+vk+=…
λk+αv+ + λk+αk+vk+=
A>

/k


ij
λiλ j

A
/k+
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;'
;'$
n

f0
(
)

f
.
n


 
 n  
5F$G
0
(
 ()
)
$$ n '
f

n=××
n$

)
0$
nC'
k
(n

k
&6'
(
v
)
( n
n

u
f
(
v((vk(vk+u(vk+((vn
)
=f
(
v((vk(vk(vk+((vn
)
+f
(
v((vk(u(vk+((vn
)
k
(n

k
&6'
(
v
)
( n
n

∀λ)
f
(
v((vk(λvk(vk+((vn
)
=λ f
(
v((vk(vk(vk+((vn
)
0 $n
n
)
0n
(
 ()
)
/$n
f
(
λv((λvn
)
=

f
(
u+v((un+vn
)
=
$$ n  '
f
$n
n
)0$
f

.+$&C&'
(
(
i(j
)
( n
{
ij
vi=vj
)
f
(
v((vi((vj((vn
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=*
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n
)
An
(
( )
)
/8$ n ) '
f
$n
n
)'
(
vi
)
i
( n
n

f
(
v((vi(vi(vi+(vj(vj(vj+((vn
)
=f
(
v((vi(vj(vi+(vj(vi(vj+((vn
)
)
n
96 
An
(
( )
)
')n
An
(
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)

)
'
An
(
( )
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
- '
 #7" 8$$&9-1
'-
f
An
(
( )
)
2. ?
g
An
(
( )
)

H=
(
((n
)


-
(
vi
)
i
( n
n
.+
n

(
αij
)
)n
+
k
(n

vk=α  k+ …+ αnkn
f
(
v((vn
)
=α  f
(
(v((vn
)
+ + αn f
(
n(v((vn
)
6
f
(
v((vn
)
=α 
(
αf
(
(((vn
)
+ …+ αnf
(
n(n((vn
))
+ …
+ αn
(
αf
(
(((vn
)
+ …+ αnf
(
n(n((vn
))
62
A6$
n

f
(
vvn
)
.>8'
αijf
(
k(kn
)

(
kl
)
(n
n
.
kl=kl'

f
(
k((kn
)
=*
6'
f
(
k((kn
)
=± f
(
((n
)
1.
k
++
 H+'
f
(
v((vn
)
=k×f
(
((n
)
)
0<2<$$ '
g
(
v((vn
)
=k×g
(
((n
)
)
5
f
(
((n
)
=*
 
f=*An
(
()
)
5'
g
(
v((vn
)
=f
(
v((vn
)
f
(
((n
)
×g
(
((n
)

(
vi
)
i
( n
n

g
(
v((vn
)
=g
(
(n
)
f
(
((n
)
×f
(
v((vn
)
$
f

g

;. ')n
(
(n
)

A.+$
f
n
n
+
f
(
((n
)
=
'.
f

,'-
f
An
(
( )
)

g
An
(
( )
)
+
f
(
((n
)
=g
(
((n
)
=
0$'
(
vi
)
i
( n
n

g
(
v((vn
)
=
×f
(
v((vn
)

f=g
$ ')n
H=
(
((n
)
 
0+$n
n
n
(
((n
)

 H
DetH
.'
u
(
*
)
H

v
(
*
*
)
H

w
(
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H

DetH
(
u(v(w
)
=
0$CC
+H 1
 8
/
DetH
')n
H=
(
((n
)
 
(
vi
)
i
( n
n

(
αk
)
)n

i
( n

DetH
(
v((vn
)
=DetH
(
v((vi(
k=
i
αkvk+vi+
k=i+
n
αkvk(vi+((vn
)
DetH
? 
'Ci&6
: 2;')
n

H=
(
((n
)

H'=
(
'(('n
)
. A'
(
v((vn
)
nDetH
(
v((vn
)
=DetH
(
'(( 'n
)
×DetH'
(
v((vn
)
'
DetHAn
(
( )
)

DetH'An
(
 ()
)
.
k)
+'
(
v((vn
)
nDetH
(
v((vn
)
=k×DetH'
(
v((vn
)

DetH
(
'(('n
)
=
 !7" 8$$&9-1
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