Unformatted text preview: × 2 matrix that changes each time you select it. Run it 10 times and determine which percentage of the matrices had real eigenvalues. You can compute the eigenvalues with the eig command each time or determine if they are real by visual inspection (which is faster). (3) The MATLAB command magic(n) produces an n × n magic square: that is, a matrix of integers from 1 to n 2 such that each row, column and the two diagonals add up to the same number. Compute the eigenvalues of the magic matrices generated by MATLAB for n = 3, 4, and 5. What do you notice about the largest eigenvalue and its corresponding eigenvector (keep in mind that MATLAB produces eigenvectors of length 1, but any multiple of them will do)? What is your conjecture about the largest eigenvalue of magic(n) for all n ? Gerardo Laﬀerriere, October 15, 2009 1...
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 Spring '09
 Lafferier
 Linear Algebra, Algebra, matlab, Matrices, Eigenvalue, eigenvector and eigenspace, Singular value decomposition, Orthogonal matrix, MATLAB command

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