# Statistics of Min-max Normalized Eigenvalues in Random Matrices

arXiv: https://arxiv.org/abs/2512.15427 · HTML: https://mlsanity.com/paper/2512.15427/

## Key facts

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- First posted on arXiv 17 Dec 2025.

## Abstract (arXiv)

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.