Recent content by Oppie

Hello, I've been using "Guide to Essential Math" by S.M. Blinder from time to time to stay on top of my basic mathematics. I'm currently on the section on Bernoulli Numbers. In that section he has the following (snippet below). Is the transition to equation 7.61 just wrong? The equation just...

Thank you. Maybe he mentions the word "adjacent" in consideration to the summation convention.

Hello, I was refreshing my Mathematics using S.M. Blinder's book "Guide to Essential Math" and on the section on Matrix Multiplication I got the following, Can someone elaborate on the highlighted section? In particular, what does "adjacent indices" mean? Thank you.

Thanks for the response. I tried looking at other books, etc. to see if I can find a better explanation on this, unfortunately there isn't, at least at all the places I searched. Also, to add, Whittaker in his Analytical Dynamics gives a proof that the action is a minimum but this requires...

Thank you. I understand it now mathematically, if that makes sense. My question now is, why require to action to be minimum? Landau and Lifshitz themselves note in a footnote that the action only needs to be stationary but now it seems that it has to be minimum for the mass to be positive.

Thanks for the bump. Unfortunately, I am still at a loss. Is it as simple as seeing that v^2 is always positive and therefore if m<0 then if v at the initial and terminal points are large then you cannot have a minimum for the action integral since it can be arbitrarily negative? Thanks.

Hello, I'm sure most of you are already familiar with the book "Mechanics" by Landau and Lifshitz. There's a section that I do not understand. In section 4 towards the end they mentions that "It is easy to see that the mass of the particle cannot be negative." They then give the argument that...