
The orthonormal basis in a tangent space

This function computes an ONB where the $\xi_1=\log_x y$ belongs to the ONB and hence it diagonalizes the curvature tensor along $\geo{x}{y}$, i.e. the eigenvalues $1$ for all $\xi_k$, $k>1$ and zero for the first value.

Matlab Documentation

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% xi = TpMONB(x,y) compute an ONB in TpM, with first pointing to q
%
% INPUT
%     x : base point( sets)
%
% OPTIONAL:
%     y : directional indicator( sets) for the first vector(s).
%
% OUTPUT
%    xi : basiscolumn matrice(s) for each TpM
%    k : (optional) curvature coefficients, here
%           all are 1 except the first which is 0
% ---
% MVIRT 1.0, R. Bergmann ~ 2014-10-19 | 2018-03-01