# A New Parametrization of Correlation Matrices

arXiv: https://arxiv.org/abs/2012.02395 · HTML: https://mlsanity.com/paper/2012.02395/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2020.

## Built on by (most cited first, 9 of 9)

- [Adaptive joint distribution learning](https://mlsanity.com/paper/2110.04829/) (2021)
- [Kernel Density Machines](https://mlsanity.com/paper/2504.21419/) (2025)
- [Entropic covariance models](https://mlsanity.com/paper/2306.03590/) (2023)
- [Riemannian Networks over Full-Rank Correlation Matrices](https://mlsanity.com/paper/2605.19073/) (2026)
- [Riemannian geometry meets fMRI: the advantages of modeling correlation manifolds and eigenvector subspaces](https://mlsanity.com/paper/2605.22334/) (2026)
- [A Sliced-Wasserstein Framework on Correlation Matrices for EEG Decoding](https://mlsanity.com/paper/2606.06104/) (2026)
- [LieBN: Batch Normalization over Lie Groups](https://mlsanity.com/paper/2607.08783/) (2026)
- [CorrFlow: Exact and Permutation-Equivariant Flow Matching on the Correlation Elliptope](https://mlsanity.com/paper/2610.13606/) (2026)
- [MAGNET: Manifold-Aware Graph Diffusion Network for Connectome Generation](https://mlsanity.com/paper/2610.17014/) (2026)

## Abstract (arXiv)

We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisther's Z-transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n x n correlation matrix from any d-dimensional vector (with d = n(n-1)/2) is provided, and we derive its numerical complexity.