Permutationen

perm=Permutations[{1,2,3,4}]

Length[perm]

sign=Map[Signature,Permutations[{1,2,3,4}]]

Transpose[Join[Transpose[perm],{sign}]]

Determinanten

A={{0,2,1},{(1/2),3,0},{5,0,2}}

Det[A]

A=Array[a,{2,2}]

Det[A]

A=Array[a,{3,3}]

Det[A]

Entwicklungssatz für Determinanten

Untermatrix[A_,{p_,q_}]:=Delete[Transpose[Delete[Transpose[A],q]],p]

Clear[Determinante]
Determinante[{{a_}}]:=a;
Determinante[A_]:=
(∑_(k=1)^(Length[A]))(((-1))^((1+k)))A[[k,1]]*Determinante[Untermatrix[A,{k,1}]]

A={{1,2,-1},{1,3,2},{2,0,1}}

Det[A]

Determinante[A]

A={{5,-8,7,9},{2,0,4,6}, {3,1,7,7},{2,8,2,5}}

Det[A]

Untermatrix[A,{2,3}]

Determinante[A]

A=Array[a,{4,4}]

det=Det[A]

Length[det]

det2=Determinante[A]

Expand[det2]

Beispiel 7.13

A={{3,2,1},{2,0,2},{1,3,4}}

Det[A]

Beispiel 7.13

A=Table[((Subscript[a, j])^k),{j,1,3},{k,0,2}]

Det[A]

Factor[Det[A]]

A=Table[((Subscript[a, j])^k),{j,1,8},{k,0,7}]

Factor[Det[A]]

Übung 7.4

Clear[A]

A[n_]:=Table[If[j==k,b,If[j-k==1,b,If[j-k==-1,1,0]]],{j,n},{k,n}]

A[5]

tab=Table[Det[A[n]],{n,10}]