01LAB1
Z WikiSkripta FJFI ČVUT v Praze
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[]\OT1/cmr/m/n/10.95 A) Ne-cht[] $\OML/cmm/m/it/10.95 n \OMS/cmsy/m/n/10.95 2$\
OT1/cmr/bx/n/10.95 N\OT1/cmr/m/n/10.95 . Vek-to-rov^^Sy pro-stor \OT1/cmr/bx/n/
10.95 T$[]$ \OT1/cmr/m/n/10.95 nad t^^Telesem \OT1/cmr/bx/n/10.95 T \OT1/cmr/m/
n/10.95 je pro-stor, kde vek-tory jsou \OT1/cmr/bx/n/10.95 uspo^^Tr^^Sadan^^Se
[]
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\OT1/cmr/m/n/10.95 2) Snadno si roz-mysl^^S^^Pme, ^^Tze po-kud to bu-deme pot^^
Trebovat, lze p^^Tri ob-vykl^^Sych ope-rac^^S^^Pch ztoto^^Tznit
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[]\OT1/cmr/m/n/10.95 Zb^^Syv^^Sa uk^^Sazat, ^^Tze lze ka^^Tzdou sou-stavu ekvi-
va-lentn^^S^^Pmi ^^Supravami p^^Trev^^Sest na sou-stavu s roz^^Ts^^S^^P^^Trenou
[]
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\OT1/cmr/m/n/10.95 (uspo^^Tr^^Sadan^^Sa $\OML/cmm/m/it/10.95 n$\OT1/cmr/m/n/10.
95 -tice) vek-tor^^Wu z \OT1/cmr/bx/n/10.95 V\OT1/cmr/m/n/10.95 . []R^^S^^Pk^^S
ame, ^^Tze vek-tor $[]$ je line^^Sarn^^S^^P kom-bi-nac^^S^^P sou-boru ($[]\OML/
cmm/m/it/10.95 ; []; [] ; []\OT1/cmr/m/n/10.95 )$,
[]
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\OT1/cmr/m/n/10.95 vek-tor^^Wu, sou-bor $([]\OML/cmm/m/it/10.95 ; []; [] ; []\O
T1/cmr/m/n/10.95 )$ se naz^^Syv^^Sa \OT1/cmr/bx/n/10.95 ge-ne-ruj^^S^^Pc^^S^^P
sou-bor \OT1/cmr/m/n/10.95 a vek-tory $[]\OML/cmm/m/it/10.95 ; []; [] ; []$
[]
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\OT1/cmr/m/n/10.95 Necht[] $([]\OML/cmm/m/it/10.95 ; []; [] ; []\OT1/cmr/m/n/10
.95 )$ je b^^Saze \OT1/cmr/bx/n/10.95 V\OT1/cmr/m/n/10.95 , tj. \OT1/cmr/bx/n/1
0.95 V$\OT1/cmr/m/n/10.95 = [[]\OML/cmm/m/it/10.95 ; []; [] ; []\OT1/cmr/m/n/10
.95 ][]$ a sou-bor $([]\OML/cmm/m/it/10.95 ; []; [] ; []\OT1/cmr/m/n/10.95 )$
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\OT1/cmr/bx/n/10.95 V\OT1/cmr/m/n/10.95 =$[[]\OML/cmm/m/it/10.95 ; []; [] ; []\
OT1/cmr/m/n/10.95 ][] = [[]\OML/cmm/m/it/10.95 ; []; [] ; []; \OT1/cmr/m/n/10.9
5 ([]\OMS/cmsy/m/n/10.95 j\OML/cmm/m/it/10.95 i \OMS/cmsy/m/n/10.95 2 [] n f\OM
L/cmm/m/it/10.95 i[]; i[]; [] ; i[]\OMS/cmsy/m/n/10.95 g\OT1/cmr/m/n/10.95 )][]
$. Sou-bor $([]\OML/cmm/m/it/10.95 ; []; [] ; []; \OT1/cmr/m/n/10.95 ([]\OMS/cm
sy/m/n/10.95 j\OML/cmm/m/it/10.95 i \OMS/cmsy/m/n/10.95 2
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\OT1/cmr/m/n/10.95 Snadno si roz-mysl^^S^^Pme, ^^Tze sou-bor $([]\OML/cmm/m/it/
10.95 ; []; [] ; []\OT1/cmr/m/n/10.95 )$ je LN a ^^Tze pro ka^^Tzd^^Sy vek-tor
$[] = [] \OMS/cmsy/m/n/10.95 2$\OT1/cmr/bx/n/10.95 T$[]$
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\OT1/cmr/m/n/10.95 Necht[] dim\OT1/cmr/bx/n/10.95 P\OT1/cmr/m/n/10.95 =$\OML/cm
m/m/it/10.95 k \OMS/cmsy/m/n/10.95 6\OT1/cmr/m/n/10.95 = 0$ $[][]\OMS/cmsy/m/n/
10.95 )$ \OT1/cmr/m/n/10.95 exis-tuje $\OML/cmm/m/it/10.95 k$ \OT1/cmr/m/n/10.9
5 LN vek-tor^^Wu $[]\OML/cmm/m/it/10.95 ; []; [] ; []$ \OT1/cmr/m/n/10.95 tak,
^^Tze \OT1/cmr/bx/n/10.95 P\OT1/cmr/m/n/10.95 =$[[]\OML/cmm/m/it/10.95 ; []; []
; []\OT1/cmr/m/n/10.95 ][]$,
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\OT1/cmr/m/n/10.95 Soubor $\OMS/cmsy/m/n/10.95 X$\OT1/cmr/m/n/10.95 = $([]\OML/
cmm/m/it/10.95 ; []; [] ; []; []; []; [] ; []\OT1/cmr/m/n/10.95 )$ ge-ne-ruje p
ro-stor \OT1/cmr/bx/n/10.95 P\OT1/cmr/m/n/10.95 +\OT1/cmr/bx/n/10.95 Q \OT1/cmr
/m/n/10.95 ze stejn^^Sych
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\OT1/cmr/m/n/10.95 (b) Opa^^Tcn^^Sa in-kluze plyne z faktu, ^^Tze \OT1/cmr/bx/n
/10.95 P \OT1/cmr/m/n/10.95 je s^^Sam pod-pro-sto-rem ob-sa-huj^^S^^Pc^^S^^Pm v
ek-tory $[]\OML/cmm/m/it/10.95 ; []; [] ; []$\OT1/cmr/m/n/10.95 .
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\OT1/cmr/bx/n/10.95 Q[] \OT1/cmr/m/n/10.95 = \OMS/cmsy/m/n/10.95 A\OT1/cmr/m/n/
10.95 (\OT1/cmr/bx/n/10.95 P[]\OT1/cmr/m/n/10.95 ) = \OMS/cmsy/m/n/10.95 A\OT1/
cmr/m/n/10.95 ([[]\OML/cmm/m/it/10.95 ; []; [] ; []\OT1/cmr/m/n/10.95 ][])$= $[
\OMS/cmsy/m/n/10.95 A[]\OML/cmm/m/it/10.95 ; \OMS/cmsy/m/n/10.95 A[]\OML/cmm/m/
it/10.95 ; [] ; \OMS/cmsy/m/n/10.95 A[]\OT1/cmr/m/n/10.95 ][]$. Z toho plyne,
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\OT1/cmr/m/n/10.95 Dok^^Sa^^Tzeme, ^^Tze pod-pro-stor \OT1/cmr/bx/n/10.95 Q\OT1
/cmr/m/n/10.95 =$[[]\OML/cmm/m/it/10.95 ; []; [] ; []\OT1/cmr/m/n/10.95 ][]$ je
do-pln^^Tek \OT1/cmr/bx/n/10.95 P \OT1/cmr/m/n/10.95 do \OT1/cmr/bx/n/10.95 V\
OT1/cmr/m/n/10.95 , tj., ^^Tze plat^^S^^P \OT1/cmr/bx/n/10.95 V\OT1/cmr/m/n/10.
95 =\OT1/cmr/bx/n/10.95 P\OT1/cmr/m/n/10.95 +\OT1/cmr/bx/n/10.95 Q
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\OT1/cmr/m/n/10.95 3) Kdy^^Tz je \OT1/cmr/bx/n/10.95 A \OT1/cmr/m/n/10.95 typu
$\OML/cmm/m/it/10.95 n \OMS/cmsy/m/n/10.95 ^^B \OML/cmm/m/it/10.95 m$\OT1/cmr/m
/n/10.95 , \OT1/cmr/bx/n/10.95 B \OT1/cmr/m/n/10.95 a \OT1/cmr/bx/n/10.95 C \OT
1/cmr/m/n/10.95 typu $\OML/cmm/m/it/10.95 m \OMS/cmsy/m/n/10.95 ^^B \OML/cmm/m/
it/10.95 p$ \OT1/cmr/m/n/10.95 plat^^S^^P z^^Sakon \OT1/cmr/bx/n/10.95 dis-tri-
bu-tivn^^S^^P \OT1/cmr/m/n/10.95 (tj. \OT1/cmr/bx/n/10.95 A\OT1/cmr/m/n/10.95 (
\OT1/cmr/bx/n/10.95 B\OT1/cmr/m/n/10.95 +\OT1/cmr/bx/n/10.95 C\OT1/cmr/m/n/10.9
5 )=\OT1/cmr/bx/n/10.95 AB\OT1/cmr/m/n/10.95 +\OT1/cmr/bx/n/10.95 AC\OT1/cmr/m/
n/10.95 ).
[]
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\OT1/cmr/m/n/10.95 Ozna^^Tcme $\OMS/cmsy/m/n/10.95 X \OT1/cmr/m/n/10.95 = ([]\O
ML/cmm/m/it/10.95 ; []; [] ; []\OT1/cmr/m/n/10.95 )$. Z de-fi-nice ma-tice zob-
ra-zen^^S^^P ply-nou vztahy $[] \OMS/cmsy/m/n/10.95 A[] \OT1/cmr/m/n/10.95 = []
(\OMS/cmsy/m/n/10.95 A[]\OT1/cmr/m/n/10.95 )[]\OML/cmm/m/it/10.95 ; \OT1/cmr/m/
n/10.95 (\OMS/cmsy/m/n/10.95 A[]\OT1/cmr/m/n/10.95 )[]\OML/cmm/m/it/10.95 ; []
; \OT1/cmr/m/n/10.95 (\OMS/cmsy/m/n/10.95 A[]\OT1/cmr/m/n/10.95 )[][]$,
[]
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\OT1/cmr/m/n/10.95 V po-sledn^^S^^Pch dvou rov-nos-tech jsme u^^Tzili jed-nak t
oho, ^^Tze sou^^Tcin li-bo-voln^^Se ma-tice od-pov^^S^^Pdaj^^S^^Pc^^S^^Pho
[]
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