
# The inner product on the hyperbolic space

Since the manifold $\mathbb H^n$ is isometrically embedded into $\mathbb R^{n+1}$ with the Minkowski metric, the inner product of twio tangent vectors $\xi,\nu\in T_x\mathbb H^n$ at $x\in\mathbb H^n$ is given by

### Matlab Documentation

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% ds = dot(x,xi,nu) inner product of two tangent vectors in TxHn
%
% INPUT
%     x  : base point (optional because all TXM are equal)
%    xi  : a first tangent vector( set)
%    nu  : a secod tangent vector( set)
%
% OUTPUT
%     ds : the corresponding value(s) of the inner product of (each triple) V,W at X
%
% ---
% Manifold-Valued Image Restoration Toolbox 1.1
% R. Bergmann ~ 2015-10-20