{VERSION 4 0 "HP RISC UNIX" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 17 "Ein Beispiel zur " } {TEXT 256 2 "LR" }{TEXT -1 10 "-Zerlegung" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart: with(linalg):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A := matrix(3,3,[0,1,2,3,4,5 ,6,7,8]);" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 80 "Vertausche erste b eide Zeilen durch Multiplikation mit einer Permutationsmatrix:" } {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "P := matrix(3,3 ,[0,1,0,1,0$4,1]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "`A'` \+ := evalm(P &* A);" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 53 "H\344nge r echts die Einheitsmatrix an und wende Gau\337 an:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "M0 := concat(`A'`, diag(1$3));" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "M1 := addrow(M0, 1, 3, -2) ; # 2*erste Zeile von der dritten subtrahieren" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 59 "M2 := addrow(M1, 2, 3); # zweite Zeile zur dri tten addieren" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "R := delco ls(M2, 4..6); # links steht R" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "L := delcols(M2, 1..3); # rechts steht L" }}}{EXCHG {PARA 259 " " 0 "" {TEXT -1 6 "Probe:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "evalm(R) = evalm(L &* P &* A);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 48 "evalm(A) = evalm(inverse(P) &* inverse(L) &* R );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 22 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }