6.48.2  Eigenvalues: egvl eigenvalues eigVl

The egvl command finds the Jordan form of a matrix.
eigenvalues and eigVl are synonyms for egvl.

• egvl takes one argument:
  A, a square matrix.
• egvl(A) returns the Jordan normal form of A.

Examples.

• Input:
  egvl([[4,1,-2],[1,2,-1],[2,1,0]])
  Output:

  ⎡ ⎢ ⎢ ⎣

  2 1 0 0 2 1 0 0 2

  ⎤ ⎥ ⎥ ⎦

• Input:
  egvl([[4,1,0],[1,2,-1],[2,1,0]])
  Output:
  See Section 6.27.21 for a discussion of rootof.

  ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

  rootof ⎛ ⎝ ⎡ ⎣ ⎡ ⎣ 1,0,−20,0,100 ⎤ ⎦ , ⎡ ⎣ 1,0,−24,0,144,0,−148 ⎤ ⎦ ⎤ ⎦ ⎞ ⎠ 18 0 0 0 rootof ⎛ ⎝ ⎡ ⎣ ⎡ ⎣ −1,0,20,18,8 ⎤ ⎦ , ⎡ ⎣ 1,0,−24,0,144,0,−148 ⎤ ⎦ ⎤ ⎦ ⎞ ⎠ 36 0 0 0 rootof ⎛ ⎝ ⎡ ⎣ ⎡ ⎣ −1,0,20,−18,8 ⎤ ⎦ , ⎡ ⎣ 1,0,−24,0,144,0,−148 ⎤ ⎦ ⎤ ⎦ ⎞ ⎠ 36

  ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

  Input:
  evalf(egvl([[4,1,0],[1,2,-1],[2,1,0]]))
  Output:

  ⎡ ⎢ ⎢ ⎣

  1.46081112719 0.0 0.0 0.0 4.21431974338 0.0 0.0 0.0 0.324869129433

  ⎤ ⎥ ⎥ ⎦