
# The logarithmic map on symmetric positive definite matrices

The logarithmic map on symmetric positive definite matrices $x,y\in\SPD{n}$ is given by

where where $\Log$ denotes the matrix logarithm.

### Matlab Documentation

1
2
3
4
5
6
7
8
9
10
11
12
% xi = log(x,y) logarithmic map at the point(s) x of points(s) y
%
% INPUT
%   x : a point or set of points on the manifold P(m)
%   y : a point or set of points on the manifold P(m)
%
% OUTPUT
%   xi : resulting point(s) of X(i) to Y(i) elementwise
%
% ---
% Manifold-Valued Image Restoration Toolbox 1.0
% R. Bergmann ~ 2015-01-20 | 2015-04-10