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Preprint analyzes lifting scalar Gaussian distances to matrices, emphasizing uniqueness and interpretations.
This is a preprint version of the manuscript "Canonical Matrix Lifts of Gaussian Statistical Distances". The paper studies when scalar statistical distances for Gaussian laws can be lifted to matrix-valued objects whose traces recover the original scalar distances. It develops uniqueness and non-uniqueness results for Mahalanobis, Bhattacharyya, and Chernoff-type Gaussian statistical distances, with emphasis on orthogonal covariance, affine covariance, matrix logarithms, Jensen-gap selection, and Fisher-geometric interpretation.
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Xin Lü (2026) studied this question.
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