anonymous
  • anonymous
Considering the Pauli matrices listed below, construct the similarity transformation S which diagonalizes the matrix. A = (0 1 1 0)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[((0 & 1 \ 1 & 0))\]
anonymous
  • anonymous
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).

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