
# The inner product on symmetric positive definite matrices

The distance on the symmetric positive definite matrices $\SPD{n}$ is given by

where $\Log$ denotes the matrix logarithm and $\lVert\cdot\rVert$ is the Frobenius norm of the matrix.

### Matlab Documentation

 1 2 3 4 5 6 7 8 9 10 11 % d = dist(x,y) compute the distance between x,y from P(n). % % INPUT % y,x : two points (matrices) or sets of points (matrices) % on P(m) % % OUTPUT % d : resulting distances of each pair of points of p,q. % --- % Manifold-Valued Image Restoration Toolbox 1.0 % R. Bergmann ~ 2014-10-19 | 2015-04-11