Statistics of Min-max Normalized Eigenvalues in Random Matrices

• URL: http://arxiv.org/abs/2512.15427v1
• Date: Wed, 17 Dec 2025 13:19:32 GMT
• Title: Statistics of Min-max Normalized Eigenvalues in Random Matrices
• Authors: Hyakka Nakada, Shu Tanaka,
• Abstract summary: This study investigates the statistical properties of min-max normalized eigenvalues in random matrices.<n>We derive the residual error that arises during matrix factorization of random matrices.
• Score: 0.7519872646378835
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Random matrix theory has played an important role in various areas of pure mathematics, mathematical physics, and machine learning. From a practical perspective of data science, input data are usually normalized prior to processing. Thus, this study investigates the statistical properties of min-max normalized eigenvalues in random matrices. Previously, the effective distribution for such normalized eigenvalues has been proposed. In this study, we apply it to evaluate a scaling law of the cumulative distribution. Furthermore, we derive the residual error that arises during matrix factorization of random matrices. We conducted numerical experiments to verify these theoretical predictions.

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