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n∈NTn
∀θ∈R, Tn(cos(θ)) = cos(nθ)
Tn
P, Q ∈R[X]
< P, Q >=Z1
−1
P(t)Q(t)
√1−t2dt
m, n ∈N< Tm, Tn>
f, g ∈ C2([0,1],R)
< f, g >=Z1
0
f(t)g(t) + f0(t)g0(t)dt
V={f∈ C2([0,1],R), g(0) = g(1) = 0}
W={f∈C2([0,1],R), f00 =f}V W
C2([0,1],R)
M2(R)
p E
p∀x∈E, kp(x)k ≤ kxk
m, n ∈N∗
A, B ∈ Mn,p(C)
< A, B >=T r(tAB)
∀A∈ Mn(C),|T r(A)| ≤ √nkAk k.k
I|f2|I
E
IC
f, g ∈E
< f, g >=ZI f(t)g(t)dt
k.k2
∀f, g ∈E, |< f, g > |≤kfkkgk
(fn) (gn)E
f g < fn, gn>
< f, g >
A, B ∈ Mn(R)< A, B >=T r(tAB)
F= a b
−b a ,(a, b)∈R2F
M2(R)
F⊥
J=1 1
1 1 F⊥
M=
1 2 3
0 1 2
1 2 3
S3(R)
H
Mn(R)
H J