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Algèbre linéaire
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Cours d'algèbre linéaire prépa/licence
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Es pace ve ct or ie lIntroduction
n
f
-
-
-
-
1 1) taut recer i peut s
î
-
-
~)
à l dee et
Ö j
û
T
-)
j
D I 7 s
"? Bso
t
Ö = 3
2
s
aco
2) Lepcouple ( arec
a la propriète ci dessus rest
s
unique
-
et
è -
=
j
fonctionne
ûzxPtBp-)
zal
+
3) 0 pourrait avoir 3 vecteurs
îsp w
inutile car
s
déjà en fo de e
etp
u On
peet voir ci
é l é m e n t a i re s
j comme ees briques qui permettent
de reconstruire iR sommme ponderées
par
5) On foire de même fo
peet arec des
ex flad
J
=
eix
briques ms wood = Leix +
gladze EIRCD EIRCE
Définition soit IK IR au C
Clk en
general esteen
corps
In
espace
vectorial sur Ik est un ensemble E non vide muni
de 2 Yois
composio interne notie quii verific
1)
- EE 2
- YEE acty Y to loi est commutative
- existe un écement neutre note OE tel que atOE =
FaEE
tBp
e
2
R
é
iv
+
P
1Pij
js
B
F
n
E
-i!'p
Béix
t")=
:"'
FOy
TY
.a
V
?
,il
x
rm
EE
aPid
x
c
, - a EE
posside un inverse pouler la loi t
FocGE F 2 quiie dip de x tg xtz 22
j
On note z en
genéral
æct (- OE
all aC 2 OE
CIE +) est un
graupe commutatif
-
t est assocative
xtCy +2)= actytz FOgY
2) lene soi de multiplica externe
CX EIKXE
Ls XxxEE
EIF EE
Ceixxeic ?1 F
-
ż
Leixtße
paspermis
dons uen E
E a
Lelx : oc tsaeix
-
permès
propriête de
- I un écement neutre c
FxEE 1
-
associativité
XCUxx =
CXM
~
multiplica
dans IRoud
=
TMX
(
=
M
-. est distributive seer t
xlact )
EIKZE =EE
- par à
rapport TIh
( + = Xxc
tux
les élements de In
s les scalaires
recters
les éliments deE s les
remarque
" XEEen general sauf siE
2) y EE axy n si E
en
general six
pas
de sens sauf
ex
E
CIK =
IIK =4
E IRR K
tz
u
to
O
TO
0
=-
od
y
c
o
"Z
ix
R
.V
tA
1xx
xa
+
C
Xo
EE
v
rb
is
d
é
X
]x
U
e
p
n
XEIR
'a
):E
IR
Q
-I,=
lK
)=
le
Kc
Rx
ilp
d
sEE
Y
E
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