$\DeclareMathOperator{\arccosh}{arccosh} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator{\Exp}{Exp} \newcommand{\geo}[2]{\gamma_{\overset{\frown}{#1,#2}}} \newcommand{\geoS}{\gamma} \newcommand{\geoD}[2]{\gamma_} \newcommand{\geoL}[2]{\gamma(#2; #1)} \newcommand{\gradM}{\nabla_{\M}} \newcommand{\gradMComp}[1]{\nabla_{\M,#1}} \newcommand{\Grid}{\mathcal G} \DeclareMathOperator{\Log}{Log} \newcommand{\M}{\mathcal M} \newcommand{\N}{\mathcal N} \newcommand{\mat}[1]{\mathbf{#1}} \DeclareMathOperator{\prox}{prox} \newcommand{\PT}[3]{\mathrm{PT}_{#1\to#2}#3} \newcommand{\R}{\mathbb R} \newcommand{\SPD}[1]{\mathcal{P}(#1)} \DeclareMathOperator{\Tr}{Tr} \newcommand{\tT}{\mathrm{T}} \newcommand{\vect}[1]{\mathbf{#1}}$

# The parallel transport on symmetric positive definite matrices

This function parallel transports a vector $\xi\in T_x\SPD{n}$ along the unique geodesic $\geo{x}{y}: [0,1] \to \SPD{n}$. The transport is given by

### Matlab Documentation

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% eta = parallelTransport(x,y,xi) parallel transport xi along g(.,x,y)
%
% INPUT
%    x : a point( set) on P(m)
%    y : a point( set) on P(m)
%   xi : a tangential vector( set, one) at (each) X
%
% OUTPUT
%  eta : tangential vector( set, one) at (each) Y
%
% ---
% ManImRes 1.0, R. Bergmann ~ 2015-01-29 | 2015-04-10