What About My Matrix Makes eig Inaccurate?

Hi all,
I want to understand what about my matrix is causing eig to return inaccurate eigensystem calculations. The code to reproduce the matrix (called ‘cov_matrix_P’) is attached below. I am wondering if it has to with the fact that there are several orders of magnitude between the largest and smallest elements in cov_matrix_P. Most importantly, I would like to know what about my matrix is causing these inaccuracies, and if possible, how I could improve the result.
N = 30;

f_matrix = zeros(N, N);
even_sum_matrix = zeros(N, N);
odd_sum_matrix = zeros(N, N);

for t = 1:N
for s = 1:N
even_sum = 0;
odd_sum = 0;

% Calculate even_sum
for r = 0:2:min(t, s)
if N-r < s-r || N-s < t-r
even_sum = 0;
continue
end
even_sum = even_sum + nchoosek(N, r) * nchoosek(N-r, s-r) * nchoosek(N-s, t-r) / (nchoosek(N, s) * nchoosek(N, t));
end

% Calculate odd_sum
for r = 1:2:min(t, s)
if N-r < s-r || N-s < t-r
odd_sum = 0;
continue
end
odd_sum = odd_sum + nchoosek(N, r) * nchoosek(N-r, s-r) * nchoosek(N-s, t-r) / (nchoosek(N, s) * nchoosek(N, t));
end

f_matrix(t, s) = even_sum – odd_sum;
even_sum_matrix(t, s) = even_sum;
odd_sum_matrix(t, s) = odd_sum;
end
end
[f_eigvector,f_eigvalues] = eig(f_matrix);
diag_elements = diag(f_eigvalues);
inverted_elements = 1./diag_elements;
f_inverse = f_eigvector * diag(inverted_elements) * f_eigvector’;

variances = [0.9236396396396394, 0.9925285285285287, 0.9966406406406404, 0.9997037037037036, 1.0001001001001, 1.0008568568568565, 1.0008568568568565, 0.9999759759759757, 1.0006766766766766, 0.9999759759759757, 1.0008568568568565, 0.9998438438438437, 1.0008568568568565, 0.992892892892893, 0.9995555555555556, 1.000676676676677, 1.001001001001001, 1.0001001001001, 0.9982942942942948, 1.0005165165165162, 0.9997037037037036, 0.9982942942942948, 0.9992352352352354, 1.0006766766766766, 0.9995555555555556, 1.000424424424425, 0.9978618618618617, 0.9984984984984983, 0.9980820820820822, 1.0001001001001];

cov_matrix_G = diag(variances);

cov_matrix_P = f_inverse * cov_matrix_G * f_inverse’;
[V,D] = eig(cov_matrix_P);
eig_check = cov_matrix_P * V – V * D;
max_error = abs(eig_check);
max_error = max(max_error(:));Hi all,
I want to understand what about my matrix is causing eig to return inaccurate eigensystem calculations. The code to reproduce the matrix (called ‘cov_matrix_P’) is attached below. I am wondering if it has to with the fact that there are several orders of magnitude between the largest and smallest elements in cov_matrix_P. Most importantly, I would like to know what about my matrix is causing these inaccuracies, and if possible, how I could improve the result.
N = 30;

f_matrix = zeros(N, N);
even_sum_matrix = zeros(N, N);
odd_sum_matrix = zeros(N, N);

for t = 1:N
for s = 1:N
even_sum = 0;
odd_sum = 0;

cov_matrix_G = diag(variances);

cov_matrix_P = f_inverse * cov_matrix_G * f_inverse’;
[V,D] = eig(cov_matrix_P);
eig_check = cov_matrix_P * V – V * D;
max_error = abs(eig_check);
max_error = max(max_error(:)); Hi all,
I want to understand what about my matrix is causing eig to return inaccurate eigensystem calculations. The code to reproduce the matrix (called ‘cov_matrix_P’) is attached below. I am wondering if it has to with the fact that there are several orders of magnitude between the largest and smallest elements in cov_matrix_P. Most importantly, I would like to know what about my matrix is causing these inaccuracies, and if possible, how I could improve the result.
N = 30;

f_matrix = zeros(N, N);
even_sum_matrix = zeros(N, N);
odd_sum_matrix = zeros(N, N);

for t = 1:N
for s = 1:N
even_sum = 0;
odd_sum = 0;

cov_matrix_G = diag(variances);

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