On the spectra of Gaussian matrices

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Abstract

We give a simple characterization of the moduli of the eigenvalues of a complex Gaussian matrix in terms of x2 distributions. We also show that the spectral radius of a k × k complex Gaussian matrix is stochastically smaller than the norm of a k × (k + 1) real Gaussian matrix. © 1992.

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Kostlan, E. (1992). On the spectra of Gaussian matrices. Linear Algebra and Its Applications, 162164(C), 385–388. https://doi.org/10.1016/0024-3795(92)90386-O

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