CFD Online Logo CFD Online URL
Home > Forums > General Forums > Main CFD Forum

Einstein's summation convention

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Display Modes
Old   February 23, 2007, 15:28
Default Einstein's summation convention
Lionel S.
Posts: n/a
Hi all,

I found a strange consistency leak in summation convections: Suppose I have two matrix, A and B

tr(AB) = (AB)_ii


(AB)_ij = A_im B_mj


tr(AB) = A_im B_mi

But if A is symmetric it means that

tr(AB) = A_mi B_mi

Which is equal to A:B, the scalar (inner) tensorial product. Which is impossible because

tr(AB) not equal to A:B even A or B are symmetric

There is a fault somewhere, but I can't find it.

Do you have an idea ? Thanx in advance...

Bye Lionel

  Reply With Quote

Old   February 23, 2007, 16:09
Default Re: Einstein's summation convention
Praveen. C
Posts: n/a
Its correct. Just work out a case of 2x2 matrices to convince yourself.
  Reply With Quote

Old   February 23, 2007, 16:28
Default Re: Einstein's summation convention
Lionel S.
Posts: n/a
Yes ... surprisingly, it works, I didn't believe it first.

... Thanx, it could help for one of my next exams (mechanics of composite materials) ;-)
  Reply With Quote


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
Span-wise summation of Fluent 3D data ayannath23 FLUENT 2 May 26, 2011 16:36
How to get cumulative summation of one field lin OpenFOAM Running, Solving & CFD 7 May 17, 2009 09:52
Sign Convention of the Total Pressure Cuong Nguyen CFX 3 June 7, 2006 16:31
File naming convention roncresswell OpenFOAM Installation 3 December 6, 2005 06:01
How to get summation of one variable at x directio zhou1 FLUENT 3 October 21, 2003 10:17

All times are GMT -4. The time now is 12:44.