Аналитическая геометрия. Шурыгин В.В. - 11 стр.

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0 · a = 0, λ · 0 = 0, (−1) · a = −a,
5
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λ ∈ R b = λa
b =
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|b|
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a a ↑↓ b
a 6= 0 b = λa λ
b a
λ =
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) (V, +, ·)
V + : V × V → V
a, b V {a, b} 7→
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λ a V
{λ, a} 7→ λ · a = λa
λ a
1
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(V, +, ·)
V
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                 0 · a = 0,   λ · 0 = 0,   (−1) · a = −a,            ‚ƃ
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   —[ -.3*L*7*,09 -.*36 00 2;,-|*,09 )0/76 ,6 b*18-3 b8*16*8\ 13-;*
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8-:-\ /7*L2J}** /b-M/8b- 1-770,*63,N b*18-3-b†
   ˜Txw™ušxXWxZ ޝ‹Œ b||a Œ a 6= 0 ¥ žŠ œ«Žž”œŽž ŽªŒž”ŽŠŽ ¤Œ‹Š
λ ∈ R ž‰ŠŽ¥ ¤žŠ b = λa =
   ‡*M/8b08*7?,-\ b = a .30 a ↑↑ b 0 b = − a .30 a ↑↓ b =
                       |b|                      |b|

   ϳTxwx™xXWxZ ޝ‹Œ a 6= 0 Œ b = λa ¥ žŠ ¤Œ‹Š λ ¢‘”Žž£ ŠžŠÄŽº
                       |a|                      |a|


ŒŽ’ ‰Š‹‹ŒŽ‘Ð ”Ž‰žŠŠ” b Œ a § ߞŠ ŠžŠÄŽŒŽ Š¬Š¢¤Žž£ ‹Žªœº
À«Œ’ Š¬¢Š’Û λ = =b
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                   a




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2;,-|*,09 b*18-36 ,6 )0/7- .30b-L98 1 /7*L2J}*;2 -.3*L*7*,0J†
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   ϳTxwx™xXWxZ 莉žŠ‘’ ¡Šžž”Š’ ( ª ¡Š‹Ž’ ”Ž«Žž”Ž‘Ð
¤ŒŽ‹) ¢‘”Žž£ žŠ¦‰ (V, +, · ) ¥ ŠžŠ£«£ Œ¢ Ž‰ŠžŠŠ©Š ’Š»Žº
ž” V Œ ª”œÐ ŠžŠ¬»ŽŒ¦Û + : V × V → V ¥ ŠžŠ£«Ž©Š ¡Ž ˎ’Žº
žŠ” a, b Œ¢ V Ž‰ŠžŠ‘¦ žŽžŒ¦ ˎ’Žž ފ©Š ’Š»Žž”¥ {a, b} 7→
a + b ¥ ¢‘”Ž’‘¦ œ’’Š¦ a Œ b ¥ Œ · : R × V → V ¥ ŠžŠ£«Ž©Š ¡º
Ž¥ ŠžŠ£«Ž¦ Œ¢ ”Ž«Žž”ŽŠ©Š ¤Œ‹ λ Œ ˎ’Žž a ’Š»Žž” V ¥
Ž‰ŠžŠ‘¦ ˎ’Žž ފ©Š ’Š»Žž”¥ {λ, a} 7→ λ · a = λa ¥ ¢‘”Ž’‘¦
¡ŠŒ¢”ŽªŽŒŽ’ λ Œ a ¥ ‰ŠžŠ‘Ž Š¬‹ªÀž ”‘ÄŽœ‰¢‘’Œ ”Š¦ž”’Œ
1 8 §
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   “7*;*,8 ;,-|*/8b6   V .30 ~8-; ,6[b6J8 ”Ž‰žŠ’Œ ‚b 6+/83618,-;
/;/7* /7-b6ƒ= ‡79 .3-/8-8 b*18-3,-* .3-/836,/8b- (V, +, · ) -+-[,6)6J8
-L,0; /0;b-7-; V =
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