Symbolic Math Toolbox

jordan

Jordan canonical form

Syntax

• J = jordan(A)
  [V,J] = jordan(A)
  

Description

jordan(A) computes the Jordan canonical (normal) form of A, where A is a symbolic or numeric matrix. The matrix must be known exactly. Thus, its elements must be integers or ratios of small integers. Any errors in the input matrix may completely change the Jordan canonical form.

[V,J] = jordan(A) computes both J, the Jordan canonical form, and the similarity transform, V, whose columns are the generalized eigenvectors. Moreover, V\A*V=J.

Examples

The statements

• A = [1 -3 -2; -1  1 -1; 2 4 5]
  [V,J] = jordan(A)
  

return

• A =
       1    -3    -2
      -1     1    -1
       2     4     5
  V =
      -1    -1     1
       0    -1     0
       1     2     0
  J =
       3     0     0
       0     2     1
       0     0     2
  

Then the statement

• V\A*V
  

returns

• ans =
       3    0    0
       0    2    1
       0    0    2
  

See Also

eig, poly

jacobian

lambertw