∗ ◦ ∗ ◦ ∗ ◦ ∗ 数学基礎演習 I ∗ ◦ ∗ ◦ ∗ ◦ ∗

2013

∗ ◦ ∗ ◦ ∗ ◦ ∗ ^{数学基礎演習} I ∗ ◦ ∗ ◦ ∗ ◦ ∗

No. 7

2013

6

6

1 (1) {a i ∈ R ⁿ⁺¹ | 1 ≤ i ≤ n + 1}

n + 1

.

i

, n

S ⁿ

U _i ^± = {x ∈ S ⁿ | ±a _i , x > 0}

.

, ·, ·

R ⁿ⁺¹

.

,

2(n + 1)

{U _i ^± | 1 ≤ i ≤ n + 1}

S ⁿ

. (2) {p(U _i ⁺ ) | 1 ≤ i ≤ n+1}

P ⁿ

.

, p : S ⁿ −→ P ⁿ

S ⁿ

∼ y ⇐⇒ y = ±x」に関する商空間

P ⁿ

.

2 A =

⎛

⎝ −1 0 1

3 2 −1

−7 −1 4

⎞

⎠ ∈ M 3 (C)

3

.

(1) xE − A =

⎛

⎝ x + 1 0 −1

−3 x − 2 1

7 1 x − 4

⎞

⎠ ∈ M 3 (C[x])

. (2) A

Jordan

3 R ²

X

α > 1

,

p ∈ R ²

,

.

(p ^α + 1) · X(p) ≤ 1.

ここで

, p

. C r = {(x, y ) ∈ R ² | x ² + y ² = r ² } (r > 0)

, X

C r

,

.

, C r

.

r→∞ lim

C

X · dl = 0.