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          |, |
      | .408248+.408248i .408248-.408248i |   | .408248+.408248i |  |
     ------------------------------------------------------------------------
     .816497          |}, {2+ii, 2-ii}, {1, 1}, | 2+i 0   |)
     .408248-.408248i |                         | 0   2-i |

o3 : Sequence

Caveat

the procedure involves computation over inexact field and hence the results may be not reliable.

Ways to use `jordanForm` :

jordanForm(Matrix)

jordanForm -- Jordan canonical form

Synopsis

Description

Caveat

See also

Ways to use jordanForm :

Ways to use `jordanForm` :