The question is how to calculate Carnot—Caratheodory (CC) norm given a signature. The equation is given in page 12 of the follwoing link: http://page.math.tu-berlin.de/~friz/master4_May6th.pdf
The |||g||| is defined in the second equation of page 12. (Do not know how to write the equation here)
Consider a signature say upto level 3;
level 1 is a vector L1= [1,2,3],
level 2 is 3 by 3 matrix M2= [1,2,3;4,5;6;7,8,9];
and level 3 is a 3 by 3 by 3
M3(:,:,1)=[1,2,3;4,5;6;7,8,9];
M3(:,:,2)=[11,12,13;14,15;16;17,18,19];and
M3(:,:,3)=[0.1,0.2,0.3;0.4,0.5;0.6;0.7,0.8,0.9];
The numbers are really arbitrary and is not representing any signature of particular path. The question is how to calculate the CC norm of this signature.
Any help would be appreciated