# What is a rotation matrix and how to implemnt it?

In Revisiting the VLAD Image Representation the authors introduce Local Coordinate System, i.e. they:

we learn off-line (for each visual word) a rotation matrix Qi from training descriptors mapped to this word.

So they obtain k (i.e. the number of visual words, or k-means parameter) rotation matrices.

My question is: how do you compute a rotation matrix given a set of descriptors?

• I think a rotation matrix is simply a matrix that rotates the x and y axes. – Michael Chernick Nov 28 '16 at 16:41
• @MichaelChernick Reading more accurately the paper, I think that they mean a simple PCA: "This is simply obtained by learning a “local” PCA per Voronoi cell of the partitioned feature space." Do you know any good solution for PCA in c/c++? – user6321 Nov 28 '16 at 16:47