T. Levi-civita and . Lezioni-di-calcolo-differenziale-assoluto, , 1925.

R. Bhatia, Positive Definite Matrices, 2007.
URL : https://hal.archives-ouvertes.fr/hal-02023293

A. Barachant, S. Bonnet, M. Congedo, and C. Jutten, Multi-class Brain Computer Interface Classification by Riemannian Geometry, IEEE Trans. Biomed. Eng, vol.59, issue.4, pp.920-928, 2012.

A. Barachant, S. Bonnet, M. Congedo, and C. Jutten, Classification of covariance matrices using a Riemannian-based kernel for BCI applications, Neurocomputing, vol.112, pp.172-178, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00820475

M. Congedo, EEG Source Analysis, Habilitation à Diriger des Recherches, University Grenoble Alpes, 2013.

F. Lotte, L. Bougrain, A. Cichocki, M. Clerc, M. Congedo et al., A Review of Classification Algorithms for EEG-based BrainComputer Interfaces: A 10-year Update, J. Neural Eng, vol.15, issue.3, p.31005, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01846433

M. Congedo, A. Barachant, and R. Bhatia, Riemannian Geometry for EEG-based Brain-Computer Interfaces; a Primer and a Review, Brain-Computer Interfaces, vol.4, issue.3, pp.155-174, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01570120

F. Yger, M. Berar, and L. F. , Riemannian approaches in brain-computer interfaces: a review, IEEE Trans. Neural Syst. Rehabil. Eng, vol.25, issue.10, pp.1753-1762, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01394253

V. Jayaram and A. Barachant, MOABB: trustworthy algorithm benchmarking for BCIs, J. Neural. Eng, vol.15, issue.6, p.66011, 2018.

L. Korczowski, M. Congedo, and C. Jutten, Single-Trial Classification of Multi-User P300-Based BrainComputer Interface Using Riemannian Geometry, Proc. IEEE EMBS, pp.1769-72, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01191913

L. Mayaud, S. Cabanilles, A. Van-langhenhove, M. Congedo, A. Barachant et al., Braincomputer interface for the communication of acute patients: a feasibility study and a randomized controlled trial comparing performance with healthy participants and a traditional assistive device, Brain-Computer Interfaces, vol.3, issue.4, pp.197-215, 2016.

P. Zanini, M. Congedo, C. Jutten, S. Said, and Y. Berthoumieu, Transfer Learning: a Riemannian geometry framework with applications to BrainComputer Interfaces, IEEE Trans. Biomed. Eng, vol.65, issue.5, pp.1107-1116, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01923278

P. Rodrigues, C. Jutten, and M. Congedo, Riemannian Procrustes Analysis: Transfer Learning for BrainComputer Interfaces, IEEE Trans. Biomed. Eng, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01971856

A. Barachant and M. Congedo, A Plug&Play P300 BCI Using Information Geometry, arXiv, 2014.

M. Congedo, M. Goyat, N. Tarrin, L. Varnet, B. Rivet et al., Brain Invaders": a prototype of an open-source P300-based video game working with the OpenViBE platform, Proc. Int. BCI Conf, pp.280-283, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00641412

A. Andreev, A. Barachant, F. Lotte, and M. Congedo, Recreational Applications in OpenViBE: Brain Invaders and Use-the-Force, pp.241-258, 2016.

M. Moakher, A differential geometric approach to the arithmetic and geometric means of operators in some symmetric spaces, SIAM J. Matrix Anal. Appl, vol.26, issue.3, pp.735-747, 2005.

Y. Lim and M. Pálfia, Matrix Power means and the Karcher mean, J. Funct. Anal, vol.262, pp.1498-1514, 2012.

M. Pálfia, Operator means of probability measures and generalized Karcher equations, Adv. Math, vol.289, pp.951-1007, 2016.

J. Lawson and Y. Lim, Weighted means and Karcher equations of positive operators, PNAS, vol.110, issue.39, pp.15626-15658, 2013.

J. Lawson and Y. Lim, Karcher means and Karcher equations of positive definite operators, Trans. Am. Math. Soc, vol.1, pp.1-22, 2014.

M. Congedo, A. Barachant, K. Koopaei, and E. , Fixed Point Algorithms for Estimating Power Means of Positive Definite Matrices, IEEE Trans. Sig. Process, vol.65, issue.9, pp.2211-2220, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01500514

B. Rivet, A. Souloumiac, V. Attina, and G. Gibert, xDAWN algorithm to enhance evoked potentials: application to brain-computer interface, IEEE Trans. Biomed. Eng, vol.56, issue.8, pp.2035-2043, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00454568

M. Congedo, L. Korczowski, A. Delorme, and F. Lopes-da-silva, Spatio-temporal common pattern: A companion method for ERP analysis in the time domain, J. Neurosci. Methods, vol.267, pp.74-88, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01343026

E. S. Edgington, Randomization tests, 1995.

F. Pesarin, Multivariate Permutation Tests with applications in Biostatistics, 2001.

P. Rodrigues, F. Bouchard, M. Congedo, and C. Jutten, Dimensionality Reduction for BCI classification using Riemannian geometry, Proc. Int. BCI Conf, pp.80-85, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01591258

M. Congedo, P. Rodrigues, F. Bouchard, A. Barachant, and C. Jutten, A Closed-Form Unsupervised Geometry-Aware Dimensionality Reduction Method in the Riemannian Manifold of SPD Matrices, Proc. Int. EMBS Conf, pp.3198-3201, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01563153

M. Congedo, B. Afsari, A. Barachant, and M. Moakher, Approximate Joint Diagonalization and Geometric Mean of Symmetric Positive Definite Matrices, PLoS One, vol.10, issue.4, p.121423, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01149652