KAJIAN MATRIKS DALAM ALJABAR MAX PLUS. Nurwan 1. PENDAHULUAN

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1 ISN : KJIN MTRIKS DLM LJR MX PLUS Nurw urw_t@ug.c.d STRK. rtl hs ttg trs d dl lr x lus srt r lsy. Ors dsr dl lr x lus dlh su ( ) d ulh ( ). Mtrs yg dhs dl rtl dlh trs t trdus. K yg dut dl rtl dlh g rlu sutu rgt trs dl lr x lus.prlu hr dr rgt trs dlh sl d c c uh rs. Kt Kuc: lr Mx Plus;Mtrs; Mtrs T Trdus; Pgt Mtrs. PENDHULUN lr x lus r udh dl lu odl d ls sutu sst tu odl tt. Hsl yg drolh ru sst yg lr shgg udh dl lu outs. Pls lh lut ttg ls lr x lus dt dlht d [][] [] d []. lr x lus ru slh stu ls dr Sst Evt Dsrt. y hl yg dt d dl lr x lus trut yg rt dg odl tt dr sutu sst vt dsrt. r slh sst vt dsrt yg tlh dlu ggu lr x lus dtry sst uftur rg tloos sst trsorts sst logst d l sgy. Sstt dr tuls dlh dwl dg ttg ls tu ggu lr x lus dl hdu shr-hr. Pd g du dr tuls hs ttg ots d dfs yg rt dg lr x lus srt gg lr x lus dl tu trs d grh. Kud d g tg dr cotoh ls dr grh dl lr x lus. Pd g t dhs rlu sutu rgt trs d dsrt dg cotoh utu h tor yg dr. Mlh rtuu utu g ttg trs dl lr x lus hususy g rlu rgt trs. Ors dsr lr x lus uy r dg ors dl lr s trsu slh trs. Ors dsr dl lr x lus dlh su yg drrsts olh d ulh drrsts olh. Ddfs d 0 d ots R x dlh hu lg rl rut: x( ) R. Du ors dsr trsut ddfs sg () Prosdg Sr Nsol Mtt d Pdd Mtt UMS 0 990

2 ISN : Prosdg Sr Nsol Mtt d Pdd Mtt UMS 0 99 Pr dr usur dsr d ors dsr dl lr x lus sg rut: ) x( ) x( () K dl ttg ors dl lr x lus dt dlht d [] d []. Ors d d R x dt drlus utu ors trs srt hy dg lr s u ors yg dgu dlh su d ulh. Ors (x)d (th) drlus trs sg rut: utu x R } { x () d utu x x R R x ] [. () Srt hly dl lr s rl trs dl lr x lus ug td outtf.pgt dl lr x lus ddfs []. sy () Utu su N dg 0. Ortor dl lr x lus uy vrs yg dyt sg gt gtf. ) ( (6) tt utu ors td l vrs. Cotoh. Dr trs d drolh su ( )trs d sdg 8 7. Dg cr yg s drolh 8 9. Dr cotoh trlht hw utu ors d trs td outtf.

3 ISN : Ddfs trs E R x (E) : = d trs R x () := ε utu st d. Rls d R x ddfs dg =. Ddfs R x := {x = [ x x... x ] T x R x =... }.Usur-usur dl Rx dsur vtor ts R x [6] d [7]. Prs rug d ggu sol lr x lus ddfs sg rut []: x( ) x( u( (6) y( C x( Nl-rtrst d vtor-rtrst dr sutu trs rsg ruur dl lr x-lus ddfs dl rs: x x x (7) x R d R d vtor rtrst d l-rtrst dr trs dg vctor x '. [] Pd g dhs sutu grh rrh dr sutu trs R. sluty dr sutu cotoh ls d dsls ggu lr x lus. Sutu grh dt strogly coctd l sutu th d utu st tt st tt. Dl hl yg d trs yg trt dg gr G ( ) d trs ttrdus. Sdg l gr G() td strogly coctd tr dlh trdus []. Cotoh. Dr sutu grhstrogly coctdsrt d Gr. x Gr : Grh G() [] Itrrts dr Gr ru lur rt yg dllu dr suh ot. Dl hl dsusu sutu dwl shgg ug rt dt lh lur d ot yg dlwty. Grh d Gr ddfs wtu rgt utu sg-sg stsu sl x ( ) d x ( ) d st yg - dg 0 drolh rs rug d sg rut [] Prosdg Sr Nsol Mtt d Pdd Mtt UMS 0 99

4 ISN : x( ) x{ x ( 8 x( } (8) x( ) x{ x ( x( } Prs (8) dt druh dl ots lr x lus sg rut: ggu ots x-lus lr ddt [] x ( ) x( 8 x( (9) x( ) x( x( Prs (9) dt druh ulsy dl tu trs sg rut: x( ) 8 x (. (0) x( ) x( Prs (0) dt dsdrh dl tu: x ( ) x( 0 () x( 8 dg x ( d x(. Sst d Prs () ru dwl rod dr lur rt yg d d Cotoh. Hl ssu dg tu r-s rut : x( ) x( ( ) x(0) 0 Utu lh lut ttg dwl dr Cotoh dt dlht d [].. METODE PENELITIN Plt ru lt ust tu tor yg rt dg lr x lus. lur lt trlht d Gr. Pdhulu Tor lr Mx Plus ls lr Mx Plus Phs Ksul Pgt Mtrs lr Mx PLus Gr. lur Plt Prosdg Sr Nsol Mtt d Pdd Mtt UMS 0 99

5 ISN : PEMHSN Pd g dhs gt trs dl lr x lus srt lht rlu dr rgt trs trsut. Mtrs yg dgu dlh trs ttrdus. Tor [] J R x dlh trs ttrdus trdt Rx 0 N c N 0 c c sd shgg ru l g dr trs d c dlh sl dr trs. Cotoh Dr trs Dg ggu tur g () dl tu trs drolh Prosdg Sr Nsol Mtt d Pdd Mtt UMS 0 99

6 ISN : J drht hsl rhtug dr Cotoh ul dr 6... trlht rgt trs yg rod. tu... uh rs c utu = d c =. Dr hsl rhtug ddt l g ( ) dlh d c=. 6. SIMPULN Prlu hr dr rgt trs dlh sl d uh rs c c. Utu sluty dt dlu ttg rlu trs trdus d ls dr rgt trs. DFTR PUSTK []. Hdrgott G.J. olsdr d J. v dr Woud (006). Mx Plus t Wor Modll g d lyss of Sychrozd Systs: Cours o Mx-Plus lgr d Its lctos Prcto Uvrsty Prss. [] utovc P. R.. Cugh-Gr (007) O Mtrx Powrs Mxlgr Lr lgr d Its lcto (007)70-8 [] F. ccll G. Coh G.J. olsdr d J.-P. Qudrt (99). Sychrozto d lrty: lgr for dscrt vt systs Wly. [] Schuttr D.. (000) O th Ultt hvor of th Squc of Coscutv owrs of Mtrx th Mx Plus lgr Lr lgr d Its lcto 07(000)0-7 [] Suoo (00) Th xstc of gvlus for rducl trcs MxPlus lgr Sr Nsol Mtt UMM Mlg [6]M. dy Rudhto (0) Sst lr x-lus trvl Wtu vrt utooous Prosdg Sr Nsol Plt Pdd d Pr MIP Fults MIP Uvrsts Ngr Yogyrt. Prosdg Sr Nsol Mtt d Pdd Mtt UMS 0 99

7 ISN : [7] M. dy Rudhto d (00) Podl lr Mx-Plus D Evlus KrJrg tr For-Jo TslDg Ksts Pygg ThggJurl Mtt Vol. No Prosdg Sr Nsol Mtt d Pdd Mtt UMS 0 996

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