ESPACES VECTORIELS DE DIMENSION FINIE 1 Dimension d`un

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K R C
{~ 0}
{~ 0}
(~u1,· · · , ~un)
{~ 0}n
{~ 0}KnKn[X]
E n ∈N∗(~u1,· · · , ~un)E
E
E n
n n E
F G E
F⊕G F ⊕Gdim(F⊕G) = dim(F) + dim(G)
dim(F+G) = dim(F) + dim(G)−dim(F∩G)
E F K
dim(E) = dim(F)Kn
Kn
E F KE f ∈L(E, F )
Ker(f)EIm(f) Im(f) Ker(f)
dim(E) = dim(Ker(f)) + dim(Im(f))
E F
f∈L(E, F )f f
f

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→H E n >1E
dim(H) = n−1
→
→
•F G E F G
F G F G
F⊕G
•E F G E F G
E F ∩G={~ 0}dim(F) + dim(G) = dim(E)
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•E n >2n−2
E n −2E