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Difference between Jordan normal form and diagonalising

  1. Nov 11, 2011 #1
    What is the difference between putting a matrix in Jordan normal form and diagonalising a matrix?

    Isn't a diagonal matrix in Jordan normal form?

    i.e what is the difference between the questions:

    Find matrices [itex]J[/itex] and [itex]P[/itex] where [itex]J[/itex] is in Jordan normal form and [itex]P[/itex] is invertible, such that [itex]A=PJP^{-1}[/itex]

    Find matrices [itex]D[/itex] and [itex]P[/itex] where [itex]D[/itex] is diagonal and [itex]P[/itex] is invertible, such that [itex]A=PDP^{-1}[/itex]
     
  2. jcsd
  3. Nov 11, 2011 #2

    Ray Vickson

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    Not every matrix is diagonalizable, but every matrix has a Jordan form (at least, if we work over the scalar field of complex numbers).

    RGV
     
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