# Euclidean Distance Between Haar Orthogonal and Gaussian Matrices

@article{GonzlezGuilln2014EuclideanDB,
title={Euclidean Distance Between Haar Orthogonal and Gaussian Matrices},
author={Carlos E. Gonz{\'a}lez-Guill{\'e}n and Carlos Palazuelos and Ignacio Villanueva},
journal={Journal of Theoretical Probability},
year={2014},
volume={31},
pages={93-118}
}
• Published 11 December 2014
• Computer Science, Mathematics
• Journal of Theoretical Probability
In this work, we study a version of the general question of how well a Haar-distributed orthogonal matrix can be approximated by a random Gaussian matrix. Here, we consider a Gaussian random matrix $$Y_n$$Yn of order n and apply to it the Gram–Schmidt orthonormalization procedure by columns to obtain a Haar-distributed orthogonal matrix $$U_n$$Un. If $$F_i^m$$Fim denotes the vector formed by the first m-coordinates of the ith row of $$Y_n-\sqrt{n}U_n$$Yn-nUn and $$\alpha \,=\,\frac{m}{n}$$α=mn…
6 Citations
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• 2016
It is well known that quantum correlations for bipartite dichotomic measurements are those of the form $${\gamma=(\langle u_i,v_j\rangle)_{i,j=1}^n}$$γ=(⟨ui,vj⟩)i,j=1n, where the vectors ui and vj
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• 2020
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SIAM J. Matrix Anal. Appl.
• 2021
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• Computer Science
ArXiv
• 2022
This work identifies that a faster paced optimization of the predictor and semi-gradient updates on the representation, are crucial to preventing the representation collapse and proposes bidirectional self-predictive learning, a novel self-Predictive algorithm that learns two representations simultaneously.

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It is well known that quantum correlations for bipartite dichotomic measurements are those of the form $${\gamma=(\langle u_i,v_j\rangle)_{i,j=1}^n}$$γ=(⟨ui,vj⟩)i,j=1n, where the vectors ui and vj
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