Results 1 to 6 of 6

Math Help - Domain of a linear operator

  1. #1
    Junior Member
    Joined
    Sep 2010
    Posts
    28

    Domain of a linear operator

    Does anyone know how to find the domain of a matrix?

    Ex:

    B=[1,0,1;5,4,9;2,4,6]

    I've tried to find a method but I don't find much on the subject.

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    The domain of an m\times n matrix is the set of all n\times p matrices, for all positive integers p. The only requirement is that the matrix multiplication be defined. The condition I've listed is the requirement necessary.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2010
    Posts
    28
    My apologies, but would you mind elaborating a little on that? If I have a 2x3 matrix I understand the domain is 3 x p but I don't think that answers the question entirely.

    Thanks for the help!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    Well, there's not a whole lot to elaborate on. You're considering the linear operator consisting of matrix multiplication on the left (that is, the operator matrix is on the left of its operand and multiplies it using regular matrix multiplication). The natural domain of a function or operator is the set of all things that you can "plug in" to the operator. For these operators, the domain is what I've described above.

    Is there some more specific portion of this for which you'd like more info?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2010
    Posts
    28
    Well my specific question is what exactly does the answer look like if I'm asked to give the domain of the matrix given in the OP? I do better with examples so I apologize if that's what you've tried to describe in words.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    A domain is a set, so I would use set builder notation. So, you've got something like

    \displaystyle \mathcal{D}(B)=\{A:A\in \mathbb{R}^{n\times p}\}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Operator
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 6th 2011, 01:29 AM
  2. Linear operator
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 30th 2011, 10:43 PM
  3. Linear Operator
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 26th 2011, 12:59 AM
  4. Linear operator #2
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 17th 2010, 01:50 AM
  5. linear operator
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 13th 2008, 09:24 PM

Search Tags


/mathhelpforum @mathhelpforum