Learning Materials
Features
Discover
Chapter 10: Q4P (page 505)
Show that the contracted tensor is a -rank tensors.
Answer
The equation has been proven.
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Show that (3.9) follows from (3.8) . Hint: Give a proof by contradiction. Let be the parenthesis in ; you may find it useful to think of the components written as a matrix. You want to prove that all 9 components of are zero. Suppose it is claimed that is not zero. Since is an arbitrary vector, take it to be the vector
, and observe that is then not zero in contradiction to
.Similarly show that all components of are zero as
claims.
Verify equations(2.6).
Show that the nine quantities (which are the Cartesian components of where V is a vector) satisfy the transformation equations for a Cartesian -rank tensor. Show that they do not satisfy the general tensor transformation equations as in . Hint: Differentiate orpartially with respect to, say,. You should get the expected terms [as in ] plus some extra terms; these extraneous terms show that is not a tensor under general transformations. Comment: It is possible to express the components of correctly in general coordinate systems by taking into account the variation of the basis vectors in length and direction.
Show that the sum of two -rank tensors is a -rank tensor. Hint: Write the transformation law for each tensor and then add your two equations. Divide out the factors to leave the result .
Write the transformation equation for a -rank tensor; for a -rank tensor
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine