(11) Pivot = 0 - ohne Pivotsuche [br] = 1 - mit Spalten-Pivotsuche [br] = 2 - mit Zeilen/Spalten-Pivotsuche[br][br]P[size=150][sub]i[/sub][/size] - Zeilen-Tausch-Matrizen ∈ Pivot[sub][size=150]i[/size][/sub], [br]L[size=150][sub]i[/sub][/size] - Matrizen für Gauß-Eliminationsschritt Spalte i ∈ Gauss[sub][size=150]i[/size][/sub], [br]Q[size=150][sub]i[/sub][/size] - Spalten-Tausch-Matrizen ∈ Pivot[sub][size=150]i[/size][/sub][br][br]L1P1AQ1 [math]\mapsto[/math][br]L1 (1.Spalte unter 1.Diagonal-Element Nullen erzeugen, [br]P1,Q1 Zeilen-Spalten-Tausch für Pivot 1. Diagonal-Element [i=1][br][br]ADD n=4[br][b](20)[/b] L2P2L1P1AQ1Q2:=Product(Gauss_{2})[br][br][b](21)[/b] Pivot_{3}:={T(3, If(Pivot==2,PivotZ(L2P2L1P1AQ1Q2, 3),Pivot==1,SPvt(L2P2L1P1AQ1Q2,3),3) ),L2P2L1P1AQ1Q2,T(3,If(Pivot==2,PivotS(L2P2L1P1AQ1Q2, 3),3) )}[br][br][b](22)[/b] P3L2P2L1P1AQ1Q2Q3:= Product(Pivot_{3})[br][br][b](23)[/b] Gauss_{3}:={Product(LE(P3L2P2L1P1AQ1Q2Q3, 3)), P3L2P2L1P1AQ1Q2Q3}[br][br][br]R=(L3 P3 L2 P2 L1 [color=#ff0000]P2 P3[/color]) ([color=#ff0000]P3 P2[/color] P1) A (Q1 Q2 Q3)[br][br][b](25)[/b] R:=Product(Gauss_{3})[br][br][b](26)[/b] L:=( Element(Gauss_{3}, 1) Element(Pivot_{3},1) Element(Gauss_{2}, 1) Element(Pivot_{2},1) Element(Gauss_{1}, 1) Element(Pivot_{2},1) Element(Pivot_{3},1) )^(-1)[br][br][b](27)[/b] P:=Element(Pivot_{3},1) Element(Pivot_{2},1)*Element(Pivot_{1},1)[br][b](28)[/b] Q:=Element(Pivot_{1}, 3)*Element(Pivot_{2}, 3)*Element(Pivot_{3}, 3)[br][br][b](29)[/b] L R = P A Q .........[br][br]SMath - MathCad Paperlike Math[br] [url=https://en.smath.com/cloud/worksheet/ELyRVLx5]LR-Zerlegung3x3MitTotalPivotSuche[math]\nearrow[/math][/url][br]