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Algèbre linéaire
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Jessica Nadeau, cours I 23 Janvier 2023
1:
Matrices CTableau
denb
)
Def une matrice de dimension mm est un tableau
:
I desements
rectangulaire de nombres constitue de m
lignes
et dem colonnes
.
p de
nb
ligne n colonne
im M
Notation A B
:
,CietC
,
clettres majuscules
)
la matrice
pour
A j
a
ann
4ais.
=I"
oz 0 a . .
dcd
z2
2s.
,
am ama ams . .
mm
,
i esélements de la matrice
sont
aij
eX
:
I
2 3 6 I
A =
2 3 -
2 vs
l
m = 2 i
a
1:2
n
=
21 az
=
B
4
3
C =
6
13
, Autres notations
:
Aman Amn
,
IaijJmxns kicm
spimension iç jem
jecolanne
i ligne
=
mest de
le nb
ligne
n est le nb dle colonnes
Remarque metn
:
Déterminer lordre dela matrice
Matrice particulière
:
une matrice nulle est one matrice on tow élement sont
leso
Notation Omxn
:
-
-
Omn 0
,
00J
Osx
ex
3-[
:
00
o
O
8}
x
1
=
3
Def
ix
une matrice
ligne u
est une matrice
:
ex Aix = t oJ
:
3
EB
21 une matrice colonne est one matrice mxI
, exB I
3x1
[ -
5
1 7
carrée
e une matrice dordre n est une matrice
ayant n
ligne et
n colonnes
.
Notation anxn
:
-
" ili
s
cm
m -
2
C 5
ex
:
E
-.2
o
DeF diagonale
-
-
principale dine matrice carrée sonties
élements an Q
33
,.a22,
2 diagonale secondaire (2 sont les
e)
a
elements
a
azn n
azin ain
-2),
-1,
,
carrée ANXN est la
somme
3) 2 trace d matrice
a
'ine
des élements de la
diagonale principale
.
TrCA +--- ann
)-Anta22
zzaii
=z
ex
}
:
-
-
l
B z o i 2
z ul 5
7 8
G
014 .8
Diagonale principale
:
secondaiib
Diaganale
:
8=17
4
T
TrCB
)
OT
matrice carrie A
DEF
tricngulaire
une est
:
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