Algebra de Vectores

Ukbtcrks y kspfbacs vkbtcrafnks

Ukbtcrks X8y X2

[o vkbtcr ko X8 c ko X2 ks uof "enkbmf" kotrk jcs puotcs, uoc nnfifjc cra`ko y ctrc nnfifjc kxtrkic quk nc jktkriaofo bcipnktfikotk. (c skf, quk sa ealfics kn cra`ko y kn kxtrkic, mfy uo scnc vkbtcr kotrk kscs jcs puotcs).

Jkeaoabaòo `kciátrabf jk uo vkbtcr

Kn bcoluotc jk tcjcs ncs sk`ikotcs jk rkbtf jara`ajcs kquavfnkotks f uo sk`ikotc jk rkbtf jara`ajc jfjc sk nnfif vkbtcr. Bufnquakr sk`ikotc jk rkbtf ko ksk bcoluotc sk jkociaof rkprkskotfbaòo jkn vkbtcr vkb tcr.. Jkeaoabaòo fn`khrfabf jk uo vkbtcr

[o vkbtcr v ko kn pnfoc ]Q ks uo pfr crjkofjc jk oüikrcs rkfnks (f, h). Ncs oüikrcs f y h sk jkociaofo knkikotcs c bcipcokotks jkn vkbtcr v. Kn vkbtcr bkrc ks kn vkbtcr (4, 4).

Ukbtcrks ealcs ko kn kspfbac [o vkbtcr ealc ks uo sk`ikotc jk rkbtf crakotfjc. Kn praikrc jk sus puotcs rkbahk kn ocihrk jk cra`ko, y kn sk`uojc, kxtrkic. Bufnquakr puotc F jkn kspfbac sk bcosajkrf bcic uo vkbtcr ealc ko kn quk bcaobajko cra`ko y kxtrkic. Zcjc vkbtcr ealc ea lc kstæ bfrfbtkrazfjc pcr su< • Iòjunc< ks nf nco`atuj jkn sk`ikotc. • Jarkbbaòo< jktkriaofjf pcr nf rkbtf quk bcotakok fn sk`ikotc y tcjfs sus pfrfnknfs. • Rkotajc< pfrf bfjf jarkbbaòo mfy jcs skotajcs pcsahnks. Kn quk bcrrkspcojk fn jkeaoajc

pcr kn rkbcrrajc jksjk F mfstf H y kn jkeaoajc pcr kn rkbcrrajc jksjk H mfstf F. kxtrkic

↘ FH cra`ko •  F

•

• H

↘ HF

 F kxtrkic

• cra`ko H

Kstcs jcs vkbtcrks takoko a`ufn iòjunc, a`ufn jarkbbaòo y skotajc bcotrfrac.

Ukbtcr nahrk Jcs vkbtcrks ealcs oc ouncs sco kquapcnkotks sa y sònc sa takoko a`ufn iòjunc, a`ufn jarkbbaòo k a`ufn skotajc. Kstf rknfbaòo ks jk kquavfnkobaf y bnfsaeabf fn bcoluotc jk ncs vkbtcrks nahrks ko bnfsks jk kquavfnkobaf nnfifjfs UKBZCX NAHXK. Zcjcs ncs vkbtcrks ouncs sco kquapcnkotks kotrk sé. Jfjc uo vkbtcr ealc, kn bcoluotc jk tcjcs ncs vkbtcrks kquapcnkotks bco án, sk jabk quk ecrifo uo vkbtcr nahrk (tcjcs takoko kn iasic iòjunc, nf iasif jarkbbaòo y kn iasic skotajc). Kn bcoluotc jk ncs vkbtcrks nahrks jkn kspfbac sk jkociaof U2. •

 

Kn vkbtcr ea lc FH ks uo rkprkskotfotk rkprkskotfotk jkn jkn  

vkbtcr nahrk  FH  FHY W Y9 u

B

H •

 

Kn vkbtcr e alc BJ ks uo r kprk kprkskotfotk skotfotk jkn jkn  

 

vkbtcr nahrk WBJY 9 v

JF