1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Science Advisor
    Homework Helper

    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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...