
# 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. Note that the basis is orthonormal with respect to the inner product in the tangent space, i.e. the Minkowski metric.

### Matlab Documentation

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% Xi = TpMONB(x,y)
% Compute an ONB in TpM, where the first vector points to y,
% whin given.
%
% INPUT
%     x : base point( sets)
% OPTIONAL:
%     y : directional indicator( sets) for the first vector(s).
%
% OUTPUT
%    Xi : basiscolumn matrice(s)
% ---
% MVIRT 1.0, R. Bergmann ~ 2014-10-19 | 2014-10-23