We can generate a random symmetric 10 10 matrix by setting A = rand(10); A = (A + A_ )/2
Chapter 7, Problem 17(choose chapter or problem)
We can generate a random symmetric 10 10 matrix by setting A = rand(10); A = (A + A_ )/2 Since A is symmetric, its eigenvalues are all real. The number of positive eigenvalues can be calculated by setting y = sum(eig(A) > 0) (a) For j = 1, 2, . . . , 100, generate a random symmetric 10 10 matrix and determine the number of positive eigenvalues. Denote the number of positive eigenvalues of the j th matrix by y( j ). Set x = 0 : 10, and determine the distribution of the y data by setting n = hist(y, x). Determine the mean of the y( j ) values, using the MATLAB command mean(y). Use the MATLAB command hist(y, x) to generate a plot of the histogram. (b) We can generate a random symmetric 10 10 matrix whose entries are in the interval [1, 1] by setting A = 2 rand(10) 1; A = (A + A_ )/2 Repeat part (a), using random matrices generated in this manner. How does the distribution of the y data compare to the one obtained in part (a)? 1
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