On the Distribution of the Roots of Certain Symmetric Matrices

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