Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Eigenvalue question

  1. May 11, 2012 #1
    Can I have a matrix that has an uncountable number of eigenvalues?
    If the matrix was infinite.
    And also can I have a matrix with a countable number of rows and an uncountable number of
    columns?
     
  2. jcsd
  3. May 11, 2012 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Sure, you can have that. But we often don't speak of "infinite dimensional matrix" anymore, but rather of a linear operator.
     
  4. May 11, 2012 #3
    Ok thanks for your answer. What about my second question?
    Can I have a matrix with a countable number of rows and an uncountable number of
    columns?
     
  5. May 11, 2012 #4

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    The yes was to both questions.
     
  6. May 11, 2012 #5
    ok thanks. Are there any other crazy interesting properties of infinite matrices?
     
  7. May 11, 2012 #6

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    The craziest property, I think, is that infinite matrices don't need to be continuous. This is quite a serious defect, since discontinuous linear maps are not so interesting.
     
  8. May 26, 2012 #7
    a matrix with countably many rows and uncountably many columns might be a linear map from functions to sequences.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Eigenvalue question
  1. Eigenvalue question (Replies: 2)

  2. Eigenvalue question (Replies: 4)

Loading...