Charakteristisches Polynom

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

χ=Det[A-λ IdentityMatrix[3]]

CharacteristicPolynomial[A,λ]

Beispiel 8.3

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

χ=CharacteristicPolynomial[A,λ]

χ/.{λ->A}

MatrixPower[A,2]+2A+7IdentityMatrix[2]

Beispiel 8.4

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

χ=CharacteristicPolynomial[A,λ]

Table[{MatrixPower[A,n]},{n,0,10}]

Beispiel 8.5

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

χ=CharacteristicPolynomial[A,λ]

Factor[χ]

Solve[χ==0,λ]

Eigenvalues[A]

Eigensystem[A]

Beispiel 8.6

A={{0,1,1},{1,0,1},{1,1,0}}

χ=CharacteristicPolynomial[A,λ]

Factor[χ]

Solve[χ==0,λ]

Eigenvalues[A]

Eigensystem[A]

Beispiel 8.7

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

χ=CharacteristicPolynomial[A,λ]

Factor[χ]

Eigensystem[A]

Beispiel 8.8

A={{0,1,1},{1,0,1},{1,1,0}}

sys=Eigensystem[A]

B=Transpose[sys[[2]]]

Inverse[B]

Inverse[B].A.B