Fizika-matematika fakulteti analitik geometriya fannidan

e^1 ,e^1

,..., e^1 bazisga o`tilgan

1

2

n

1

2

n

bo`lsin. U holda

bazislarni teskari

almashtirishiga

(3)

matritsa mos keladi

x

qaralayotgan R chiziqli fazoning ixtiyoriy elementi bo`lsin. (x₁ , x₂ ,...,x_n ) esa uni

e ,e ,...,e

bazisdagi

koordinatasi

(x^1

, x^1

,...,x^1 )

esa

e^1

,e^1 ,..., e^1

bazisdagi

1

2

n

1

2

n

1

2

n

koordinatasi bo`lsin, ya`ni

x

x^1e^1

x^1e^1

...

x^1 e^1

x e

x e ...

x e

1 1

2 2

n n

1 1

2 2

n n

e1 ,e2 ,...,en

lar o`rniga ularni (4) dagi ifodalarini qo`yib

x

x^1e^1

x^1 e^1

...

x^1 e^1

x (

^A11

e^1

^A21

e^1

...

^An1

e^1 )

d

d

1 1

2 2

n n

1

1

d

2

n

x

(

^A12

e^1

^A22

e^1

...

^An 2

e^1 ) ...

x

(

^A1n

e^1

^A2 n

e^1

...

^Ann

e^1 ).

2

n

d

1

d

2

d

n

d

1

d

2

d

n

Oxirgi tenglikdan

e^1

,e^1

,..., e^1

bazis bo`yicha yagona yoyilma o`rinli ekanligidan

1

2

n

(x , x ,...,x ) koordinatadan

(x^1 , x^1

,..., x^1 )

koordinataga

o`tish

formulasi kelib

1

2

n

1

2

n

chiqadi:

15

x^1

^A1 1

x

^A1 2

x

....

^A1n

2

1

d

1

d

d

x^1

^A2 1

x

^A2 2

x

....

^A2 n

2

2

d

1

d

d

.......... .......... .......... .......... ......