jordanForm -- Jordan canonical form

Synopsis

• Usage:

  jordanForm(A)

• Inputs:
  • A, a square matrix.
• Optional inputs:
  • Tolerance => ..., default value .001, numerical tolerance.
• Outputs:
  • chBasMatr, the matrix that transforms A in Jordan form.
  • sepEigen, the generalized eigenvectors.
  • eigNrep, the eigenvalues of the matrix A.
  • algMult, the algebraic multiplicity of each eigenvalue.
  • jorFor, the Jordan form of A.

Description

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : A = matrix{{1,2},{-1,3}}

o2 = | 1  2 |
     | -1 3 |

              2        2
o2 : Matrix ZZ  <--- ZZ

i3 : (pCh,sepEigs,peigs,palgm,JF) = jordanForm(A)

o3 = (| .816497           .816497           |, {| .816497           |, | .816497           |}, {2+ii, 2-ii}, {1, 1}, | 2+ii 0   
      | .408248+.408248ii .408248-.408248ii |   | .408248+.408248ii |  | .408248-.408248ii |                         | 0    2-ii
     ----------------------------------------------------------------------------------------------------------------------------
     |)
     |

o3 : Sequence

Caveat

See also

• compMatr -- companion matrix
• solveSystem -- solutions to a system of equalities