Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Mathematics
General Math
Einstein summation convention confusion
Reply to thread
Message
[QUOTE="dyn, post: 6514888, member: 501581"] Hi If i have a vector [B]r[/B] = ( x[SUB]1[/SUB] , x[SUB]2[/SUB] , x[SUB]3[/SUB]) then i can write [B]r[/B][SUP]2[/SUP] as x[SUB]i[/SUB]x[SUB]i[/SUB] where the i is summed over because it occurs twice. Now is x[SUB]i[/SUB]x[SUB]i[/SUB] the same as x[SUB]i[/SUB][SUP]2[/SUP] ? I have come across an example where they are used as equivalent but i am confused because x[SUB]i[/SUB][SUP]2[/SUP] seems to be the square of just one component of [B]r [/B]but x[SUB]i[/SUB][SUP]2[/SUP] also seems to be logically the same as x[SUB]i[/SUB]x[SUB]i[/SUB] My other question is ; are there some quantities that cannot be written in summation convention ? Such the kinetic energy of many particles . I have seen it written using sigma notation as the sum over k from 1 to N as m[SUB]k[/SUB][B]v[SUB]k[/SUB]v[SUB]k[/SUB] [/B]but obviously k appears 3 times here. This applies to small oscillations where the [B]r[SUB]k[/SUB] [/B]is differentiated with respect to different variables . Are some quantities impossible to write in summation convention ? Thanks [/QUOTE]
Insert quotes…
Post reply
Forums
Mathematics
General Math
Einstein summation convention confusion
Back
Top