Matrices de to

8/2/2019 Matrices de to

1/26

OALIOAK# ^FCAXAOKQ O\CX\TK

JKXTAOL_ HL ^LI_KJALIXF

Q LC IF_FXTF_

CKXAIFKJLTAOKIF


2/26

If ls ~fsadcl ck oalioak k~fcxaok# sai

ahlfcf`k# il|xtkc# {|l hlsokcaea{|l kfxtfs ofifoajalixfs ofjf ~fcxaofs#ahlfc`aofs# ukcftkxaufs q ~ft lccf

~tloalixaeaofs)

CK OFIXTFULT_AK XLFTAOKL_ \I HLDKXL ^FCAXAOF


3/26

[| ls |ik jkxtaw hl ~liskjalixf6

Jkxtaw xltaof ~fcxaok) Ktxao|ckoai hl |iofig|ixf hl okxl`ftks q ukcftls ofisxax|xaufs{|l ofieftjki ck xtkjk c`aof*ofioalixl dsaokq lsxkdcloli cfs e|ihkjlixfs hl |ikhlxltjaikhk ofttalixl hl ~liskjalixf

Eftjks hl tllckdftkoai q sasxljkxawkoaiofiol~x|kc hl hlxltjaikhks ~ltol~oafils hlcj|ihf# ahlktafs q ks~atkoafils# {|l xalili

tka`kjdtl li ~tfolsfs basxtaofs q lr~ltalioaks~fcxaoks# q sl kcajlixki hl s|sxtkxfs o|cx|tkcls{|l lrolhli cfs jktofs lsxtaoxkjlixlaixlclox|kcls f oalixeaofs)


5/26

HAELTLIOAK LIXTL CK_JKXTAOL_7

OFIOL^OAFI HL

CF _FOAKC Q HLCF ^FCXAOF


6/26

JKXTAOL_ HL CF_ ^KA_L_

OLIXTKCL_k! CADLTKC

k);) Eacfseaofg|thaok

k)4) Lofijaok

d! JKTRA_XK


8/26

k)4)JKXTAW CADLTKC

LOFIFJAOK If bkq ofixtkxf# saif kooafils aihauah|kcls)

Jkif aiuasadcl

Ikx|tkclwk

Clqls fdglxauks

Lsxkhf if aixltulioafiasxk

Oalioak fdglxauk7 hlso|dtl clqls ikx|tkcls


9/26

d! JKXTAW JKTRA_XK

Bfjdtl if sfcf ofjf oa|hkhkif hl cka`|kchkh q ck cadltxkh# saif xkjdai ofjf~tfh|oxft)

^ckixlf hl cks hlsa`|kchkhls sfoakcls) Bfjdtl ofjf slt sfoakc7 o|lsxafik ck

ikx|tkclwk)

Ck ikx|tkcawkoai hl ck sfoalhkh kxtad|ql k cfsfdglxfs ~tf~alhkhls {|l ofttls~fihli k ckstlckoafils tls|cxkixls hl ~tfolsfs basxtaofs)


10/26

_l o|j~cli qk oaiof sa`cfs hlshl {|l lsl

ikul`kixl uasafiktaf q xfw|hf kttadktk kcks ofsxks hl i|lsxtf ofixailixl=~ltsfikcawkoai hlc ls~tax| hl s| ~fok#bagf q ~tfxk`fiasxk hlc ~tajlt ~tfolsfoauacawkxftaf hl kcokiol j|ihakc) Q lc c|`kt{|l ~|hf ofie|ihatsl ofi lc ^ktksf sltaklsoliktaf hl |i hackxkhf htkjk basxtaof

hfihl sl lixtljlwocktfi kulix|tltfs qlsockufs# aih`liks q sl`|ihfils


11/26

l|tf~lfs hlsbltlhkhfs hl hasjacls

o|cx|tks# tkdls# gk~filsls# t|sfs#ktjliafs# g|hfs# oftlkifs f obaifs)Xalttk hl hfcft q hl ls~ltkiwks# hlhlsftdaxkhks e|safils `lixaoks# ~fok

h|hk okdl koltok hl ck blxltf`ilkofj~fsaoai hl |ik ahlixahkhckxaifkjltaokik ~tf~ak hl lsxfs

xlttaxftafs# |iaeaokhfs fta`aikcjlixl li lc~tfolsf xtk|jxaof hl ck ofi{|asxk q ckofcfiawkoai


13/26

Li cks ultxalixls hlc ~liskjalixf ~f~|cktckxaifkjltaokif lsk otasas sl bk jkiaelsxkhf

basxtaokjlixl li ck kixaifjak lixtl cks~tf~|lsxks l|tf oixtaoks hl ck oauacawkoai# lc

~tf`tlsf# ck a`|kchkh# ck cadltxkh# ck sfdltkik f ckjfhltiawkoai# etlixl k ck ~ltsasxlioak hl ck

s|dfthaikoai xiaok q o|cx|tkc q cks htkjxaokssax|koafils k {|l e|ltki sfjlxahks cks jkqftks

sfoakcls li ifjdtl hl k{|lccks ofiol~oafils)[|l ls xkjdai lsk ekckoak hl f~filt lc ~tf`tlsfetlixl k ck g|sxaoak q ck k|xfifjk ~ckixlkhk li

K)C) hlshl bkol hfs sa`cfs ~ft cks ofttalixlscadltkcls# ofi cks khk~xkoafils q oktkoxltsxaokshl okhk ~ltafhf basxtaof hl tlktxao|ckoai

ofcfiakc)"Kt`|jlhf# ~k`);25!


14/26

[\L OFIOL^OAFI HL CF_FOAKC JKTOK CKHAELTLIOAK LIXTL CKJKXTAW CKXAIFKJLTAOKIKIKOAFIKC Q ^F^\CKT QFXTK_6


15/26

Xtls hajlisafilsk xlilt li o|lixk li ck ofiol~oai hl

sfoalhkh7 Oktkoxltsxaoks hl ck lsxt|ox|tk sfoakc q hlc

hlskttfccf kcokiwkhf ~ft cks e|ltwks ~tfh|oxauks#tlckoafils hl ~tfh|ooai# hasxtad|oai hl ckta{|lwk)

Ahlixahkhls o|cx|tkcls) _l tleftj|ck lcslixahf hl ck basxftaoahkh) Lc ~tf`tlsf if lsil|xtf# bkq {|l aioft~ftkt ck ~tl`|ixk sfdtl lc{|ails# lc ojf# q {| sa`iaeaok hlshl cfsukcftls hl sfdltkik q g|sxaoak)

Tlckoafils lixtl sfoalhkhls li lc hluliat hlck basxftak)


16/26

CF ^FCXAOF LI CK_ JKXTAOL_ HL CF_^KA_L_ OLIXTKCL_

k! CADLTKC

k);) Eacfseaof g|thaok7 k|xfifjk hlcf ~fcxaof

k)4) Lofijaok7 hl~lihlioak hl cf~fcxaof k cf lofijaof

d! JKTRA_XK7 cf ~fcxaof ofjf ljlt`lixl f tleclgfhl ck lsxt|ox|tk lofijaok) @tkjsoa q Jkfaiaoaktfi |ik ofiol~x|kcawkoai koltok hl ck~tajkok hl cf ~fcxaof)


17/26

CF ^FCAXAOF OFJF OKXL@FTAKKTXAO\CKHFTK HL CK_ HAJLI_AFIL_ HL

CF _FOAKCCf ~fcxaofofjf ofj~clgk ofiea`|tkoai hl

hasxaixks jkiaelsxkoafils hl ~fhlt)Aioc|ql ck ~fcxaokofjf ofig|ixf hl

elijlifs js ca`khfs k cktl~tlslixkxauahkh q k ck ft`kiawkoaiaisxax|oafikc)

Ck ~tajkok hl cf ~fcxaof tlofifol ckk|xfifjk tlckxauk hl cks haeltlixlslseltks hl ck uahk sfoakc q s|s ls~loeaoksjkiaelsxkoafils hl ~fhlt)


18/26

Cf ~fcxaof sl ta`l ~ft ck c`aok hl ck off~ltkoai flc kixk`fiasjf lixtl ufc|ixkhls ofcloxauks) _ixlsas

{|l aioft~ftk cks ofixtkhaooafils)

aioft~ftk cfs lcljlixfs lofijaof*jkxltakcls~ltf if ls |i jltf ljlt`lixl hl cfs jasjfs=

oficcluk ofiol~oafils hlc j|ihf l ahlfcf`ks ~ltfif sl tlsxtai`l k lccks

Aj~ftxkioak hlc kofixloajalixf o|kihf ck ec|ahlw q

ofj~clgahkh hl cf ~fcxaof xalihl k aiuasadacawktsl) Ckc`aok hlc kofixloajalixf aj~caok {|l |i hlxfikixltleftj|ck lc ~tfolsf basxtaof kixltaft q ~tfh|ol |ilsoliktaf haeltlixl)


19/26

Ck ikoafikcahkh~|lhl slt |ik eftjk basxtaok

hl ahlixaeaokoai) _l ~ckixlki haultsks eftjks hlkhsota~oai l ahlixaeaokoafils {|l sl ultxldtkihl jfhf ofj~clgf# q if |ik iaok ahlixaeaokoaikdktokhftk q lroc|qlixl)

Hfdcl ofiecaoxauk7 cf sfoakcq cf ikoafikc)

Cfs ~tfdcljks olixtkcls hl Ckxaifkjtaok7 ck

sfdltkik q ck g|sxaoak# ofjf eftjksofcloxauks hl ck cadltxkh q ck a`|kchkh)


20/26

LC ^\IXF HL UA_XK ^F^\CKTCKXAIFKJLTAOKIF

Tlo|~ltk kcxltahkhls lroc|ahks ~ft cksofttalixls l|tf oixtaoks)

Tlofifoajalixf hlc fxtf basxtaofjlifs~tloakhf# ck uasai hl cfs ulioahfs

\i s|glxf sfoakc blxltf`ilf {|l xalil

|ik basxftak ofji hl tlsasxlioaks qhls`kttkjalixfs)


22/26

KC@\IF_ HA_O\T_F_

^KTK OFJ^TLIHLT Q

^TFDCLJKXAWKTCK JKXTAW CKXAIFKJLTAOKIK


23/26

Lc Lsxkhf if ls |i ofixtkxf ia s| lslioak

s|sxkioakc ls ck hlelisk q `ktkixk hl ckuahk q ck ~tf~alhkh hl cfs aihauah|fs ofjf~ltsfiks li eftjk aiofihaoafikc= js dalils cf js lclukhf {|l xkjdai ~tlxlihl

lsk uahk q lsk ~tf~alhkh q lra`l lcskotaeaoaf hl ck jasjk

Bl`lc# ;24;# Cilks e|ihkjlixkcls hlcHltlobf)


24/26

Cfs kdft`lils kjltaokifs sfi |ik tkwk hdac li~tfolsf hl hlsk~ktaoai) _|s t|hajlixktaks

oauacawkoafils xliki {|l hlsk~ktloltilolsktakjlixl k ck ccl`khk hl ck aiofj~ktkdcloauacawkoai l|tf~lk) Q ks ofjf s| o|cx|tk ltkhl okcahkh aieltaft# ks {|alils sa`|altfi salihf

skcukgls cf e|ltfi li `tkhf s|jf7 sfi cksj|lsxtks js kokdkhk hl ck ekcxk hl

oauacawkoai)

Bl`lc# Clooafils sfdtl ck eacfsfek hl ck basxftak|iaultskc)


25/26

Xfhkuk jks haeoac ~tlslixat ck s|ltxl e|x|tk hlci|luf j|ihf ofjf lsxkdclolt ~taioa~afs sfdtls| ~fcxaok# q oksa ~tfelxawkt ck ikx|tkclwk hlc`fdaltif {|l ccl`kt k xliltLc lj~ltkhftOktcfs U eftj |i ~koxf ofi cfs hlso|dtahftls#

ofi{|asxkhftls q ~fdckhftls hl Kjtaok {|l#ofjf haol @|lttk# ls i|lsxtf Ofixtkxf _foakc

Hlslf js {|l fxtf kc`|if ult eftjkt liKjtaok ck js `tkihl ikoai hlc j|ihf#

jlifs ~ft s| lrxlisai q s| ta{|lwk# {|l ~ft s|cadltxkh q s| `cftak

Dfcaukt# Oktxks hl Gkjkaok# ;2;


26/26

[|ai {|l bk uasxf kwfxkt k |i il`tf ifsl ofisahltk ~ktk salj~tl s| hl|hft6 Qfcf ua# cf ua o|kihf ltk iaf# q xfhkuk if

sl jl bk k~k`khf li cks jlgaccks ckult`liwk Qf cf ua q jl g|tl hlshl

lixfiols s| hlelisk

Gfs Jktxa

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