https://preview.redd.it/v8h3opqutq9d1.png?width=543&format=png&auto=webp&s=a0a4c24faa2d2fec2be1e96d0a081c1f31fa0c00

https://preview.redd.it/zuvlwywvtq9d1.png?width=538&format=png&auto=webp&s=c4ea1a653903e471d706f20324ea6bc9506b8979

The pages above discussed how to construct the matrix A that relates the elongations of each springs, e_i, and the movements of the masses, m_j.

I understood the material that's presented on these pages, and I do get the physical intuition behind the equations. For example e_2= u_2 - u_1 because suppose m_1 didn't move in a moment of time and m_2 moves downwards, then u_2 is ( ) and u_1 is 0 and the second spring will be stretched which corresponds to a ( ) elongation. But I have a problem in this subsection when the text starts discussing about circles of springs.

https://preview.redd.it/2h8llpr2vq9d1.png?width=547&format=png&auto=webp&s=db9e7a953e0c8a63f61c26d35b4799a0d64ab53e

Based on the given matrix A, why is the first equation of the system e=Au is e_1=u_1 - u_3 and not e_1=u_3 - u_1?

Why is that when u_3 moves downwards and let's say u_1 is fixed for a moment of time, the spring that connects mass 1 and 3 becomes compressed (elongation e_1<0)? Shouldn't it be stretched? Can you help me understand the physical intuition behind this equation e_1=u_1 - u_3 ?