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Row reduction and linear maps

  1. Dec 30, 2007 #1


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    Hi, everyone:

    I was wondering about the relation of a matrix , seen as a linear map,
    and its row-reduced form, seen the same way.

    More specifically: take a matrix M , seen as a linear map L. What
    is the relation between this map L given by M, and the linear map L'
    given by M', the row-reduced form of M. Are these maps L,L' equal?
    Are L,L' related in some other way?.

  2. jcsd
  3. Dec 30, 2007 #2
  4. Dec 30, 2007 #3


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    Indeed, any invertible matrix can be row reduced to the identity matrix, precisely because they both have the entire space as image (row space).
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