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Eigenvalue spectrum support of paired random matrices with pseudo-inverse

Published 26 Jun 2025 in math.SP, cond-mat.dis-nn, and math.PR | (2506.21244v2)

Abstract: The Moore-Penrose pseudo-inverse $X\dagger$, defined for rectangular matrices, naturally emerges in many areas of mathematics and science. For a pair of rectangular matrices $X, Y$ where the corresponding entries are jointly Gaussian and i.i.d., we analyse the support of the eigenvalue spectrum of $XY\dagger$.

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