On the Distribution of the Roots of Certain Symmetric Matrices

1958/03/01 by Eugene P. Wigner, E. P. Wigner · 1,512 citations
Computer Science · Mathematics · #Distribution (mathematics) #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Pure mathematics

paper · doi:10.2307/1970008

published in Annals of Mathematics 67(2), 325 (Princeton University)

openalex publication_date 1958/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

The present article is concerned with the distribution of the latent roots (characteristic values) of certain sets of real symmetric matrices of very high dimensionality. Its purpose is to point out that the distribution law obtained before' for a very special set of matrices is valid for much more general sets. The dimension of the matrices will be denoted by N, the matrix elements by via. These are real. The condition of symmetry is

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