
# The inner product on the sphere

Since the manifold $\mathbb S^n$ is isometrically embedded into $\mathbb R^{n+1}$ we obtain the inner product of two tangential vectors $\xi,\nu\in T_x\mathbb S^n\subset\mathbb R^{n+1}$ from the embedding space.

### Matlab Documentation

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% ds = dot(x,xi,nu) inner product of two tangent vectors in T_xSn
%
% INPUT
%     x  : a point(Set) in P(n)
%     xi  : a first tangent vector( set) to (each) x
%     nu  : a secod tangent vector( set) to (each) x
%
% OUTPUT
%     ds : the corresponding value(s) of the inner product of
%     (each triple) xi,nu at x
%
% ---
% MVIRT 1.0 ~ J. Persch 2016-06-13