https://www.nicovideo.jp/watch/sm35236499 https://youtu.be/yoHWx9agnH0

1. Re:

2. – –
“
– ”

3. “ ”
ESS

4. WORD

5. x = (x1, x2, ⋯, xn) ∈ Δn−1
x1 x2 x3
n
∑
i=1
xi = 1
xn
…

6. i j
n×n A
i
f(i, x) ≡ et
i Ax =
n
∑
j=1
aijxj
aij = f(i, j) aij
et
i = (0, 0, ⋯, 0, 1, 0, ⋯,0)
{i

7. vs
a12
➡ a21
vs
a13
➡ a31
a12
a21 a22 a23
a11 a13
a31 a32 a33
x1
x2
x3
x1 x2 x3
f(1,x) = (1,0,0)
a11 a12 a13
a21 a22 a23
a31 a32 a33
x1
x2
x3
= (a11, a12, a13)
x1
x2
x3
= a11x1 + a12x2 + a13x3
f(i, x) ≡ et
i Ax =
n
∑
j=1
aijxj
A
{
et
1 = (1, 0, 0)
{
A

8. f(x, x) ≡ xt
Ax =
n
∑
i=1
n
∑
j=1
xiaijxj
a12
a21 a22 a23
a11 a13
a31 a32 a33
x1
x2
x3
x1 x2 x3
A
f(x, x) = (x1, x2, x3)
a11 a12 a13
a21 a22 a23
a31 a32 a33
x1
x2
x3
= (x1a11 + x2a21 + x3a31, x1a12 + x2a22 + x3a32, x1a13 + x2a23 + x3a33)
x1
x2
x3
= (x1a11 + x2a21 + x3a31)x1 + (x1a12 + x2a22 + x3a32)x2 + (x1a13 + x2a23 + x3a33)x3
= x1a11x1 + x2a21x1 + x3a31x1 + x1a12x2 + x2a22x2 + x3a32x2 + x1a13x3 + x2a23x3 + x3a33x3

9.
i
i x’ x′i = xi
et
i Ax
xtAx
et
i Ax * xiV
{
{
V
xt
AxV{ ixiV

10. (=V)
3
0 0 4
1 5
4 0 0
x1 = 0.1
x2 = 0.5
x3 = 0.4
0.1 0.5 0.4
A
x1V
x2V
x3V
et
1Ax
et
2Ax
et
3Ax
et
1Ax * x1V
et
2Ax * x2V
et
3Ax * x3V
x′1 = x1
et
1Ax
xtAx

11. i
Δxi = x′i − xi = xi
et
i Ax
xtAx
− xi = xi
et
i Ax − xt
i Ax
xtAx
“ ”
Δxi
dxi(t)
dt
≡ ·xi = xi
et
i Ax − xt
i Ax
xtAx
·xi = xi(et
i Ax − xt
Ax), i = 1, ⋯, n

12.
Δn−1
·xi = xi(et
i Ax − xt
Ax), i = 1, ⋯, n{
{
et
i Ax xt
Ax
i ” ”

13.
·xH = xH(et
H Ax − xt
Ax) = xH(et
H − xt
)Ax
·xi = 0 x
1 − xH
xH
1 − xH
xH
= xH(1 − xH)(1, − 1)
(
−1 4
0 2) (
xH
1 − xH)
= xH(1 − xH)(2 − 3xH)
= xH(1 − xH)(1, − 1)Ax
·xH = 0 ⇒ xH = 0,
2
3
, 1
xH
0 1
2
3
·xH(t) > 0 if xH <
2
3
·xH(t) < 0 if xH >
2
3
2/3 ESS

14. ESS
ESS
ESS
WORD
xH
0 1
2
3
·xH(t) > 0 if xH <
2
3
·xH(t) < 0 if xH >
2
3

15. – See you next time!–