Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

kirbykirby

  • one year ago

Linear Algebra/Linear Regression: The Hat matrix is defined as \(H=X(X^TX)^{-1}X^T\). Messing with it a bit I found that it was equal to the identity matrix o_O? Can you show me where I went wrong?

  • This Question is Closed
  1. kirbykirby
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It shouldn't be though since this matrix is significant for linear regression. (I mean why would they define such a long expression?). \[X(X^TX)^{-1}X^T\]=\(X(X^{-1}(X^T)^{-1})X^T\)\[=X(X^{-1}(X^{-1})^{T})X^T\]\[=XX^{-1}(X^{-1})^TX^T\]\[=I(X^{-1})^TX^T\]\[=I(XX^{-1})^T\]\[=II=I\]

  2. KingGeorge
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Took a little research, but you're correct. However, if \(X\) does not have an inverse, this does not result in the identity.

  3. KingGeorge
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    See here for a little more information http://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse

  4. kirbykirby
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    o_o interesting. Hmm lol this Hat matrix is a lot more special than I thought lol

  5. KingGeorge
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Same here.

  6. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.