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A note on the volume form in normal matrix space - Docentes - professor ufabc edu

A note on the volume form in normal matrix space - Docentes - professor ufabc edu 2025

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The document presents a local parametrization of the Riemann volume form in normal matrix space using spectral variables. It details the algebraic method for expressing the volume form in terms of eigenvalues and skew-Hermitian matrices, emphasizing the unitary invariance of normal matrices. The authors derive the Jacobian for the coordinate change from matrix elements to spectral coordinates, which is crucial for understanding eigenvalue statistics in random normal matrices.

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