Eigenvalue distribution relation

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The discussion centers on the relationship between the diagonal elements of a random matrix, denoted as H_{ii}, and their corresponding eigenvalues, λ_{i}. There is confusion regarding the term "corresponding eigenvalue" and how eigenvalues relate to specific positions within the matrix. Participants seek clarification on whether the distribution of diagonal elements matches that of eigenvalues. The conversation highlights the need for a clearer understanding of eigenvalue positioning in relation to matrix elements. Overall, the inquiry emphasizes the complexities of eigenvalue distribution in random matrices.
nikozm
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Hello,

I was wondering if H_{ii} (that is the ith diagonal element of a random matrix) has the same distribution with its corresponding eigenvalue, say \lambda_{i}.

Thanks
 
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I don't know what you mean by 'its corresponding eigenvalue". How does and eigenvalue "correspond" to a position in a matrix?
 

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