A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Considering the Pauli matrices listed below, construct the similarity transformation S which diagonalizes the matrix. A = (0 1 1 0)

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[((0 & 1 \ 1 & 0))\]

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    A and B are similar if there is some matrix P such that B = P*A*inv(P). Have you heard of eigenvalues and eigenvectors? They can be used to diagonalize square matrices with n linearly independent eigenvectors. first, find the eigenvalues of A. They will be -1 and 1. Then find the corresponding eigenvectors. For lambda = -1, we get v1 = (1, -1) (column vector) For lambda = 1, we get v2 = (1, 1) (column vector). So now let Q be the matrix with columns v1 and v2. Let D be a diagonal matrix with first entry -1 and second entry 1, ie. the corresponding eigenvalues to the eigenvectors of Q. Then A = Q*D*inv(Q).

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.