# James Ebhabha

James Ebhabha wrote on the scalar triple product of the base vectors. Here is my response:

Please let me have a feedback on this post. Students who want to discuss details can send me their fully typeset comments using the Microsoft equations editor through my email address. I will paste their questions with my response on this page so to benefit other students.

# Tensor Calculus

Here are the slides on Tensor Calculus

# An Example of Cayley-Hamilton

You can also try these and make your comments here.

# Further on Cayley-Hamilton

Consider the following Mathematica code. Try it out and see what I am trying to do here by using the Cayley-Hamilton to get the inverse of a matrix without going through the usual co-factor route:

Can you try it out.

# Secondary School Students & Cayley-Hamilton

Did you think I was taking you too far into mathematics when I taught the Cayley Hamilton theory in our last class. I think not! But you may not believe me. But what if I told you that secondary school pupils know this theorem? You better believe it because I have a proof! Just look at this web blog:

http://sahilmohnani.wordpress.com/2013/04/12/the-cayley-hamilton-theorem-its-applications/

and tell me what you think about it.

# Taiwo Atinsola

Hello Taiwo,

You made a valiant effort to obtain the component representation of the third invariant of the second-order tensor. You are generally on the right track but you did not express the scalar product completely in the component form as you should have done. Since a scalar triple product is a scalar, you should be able to express it completely without any vector basis. I have decided to work it out fully for the class and my notes from now on will carry the explanation I am supplying below:

This should provide a complete answer to what you were trying to do. If you have further questions, please comment below.

# Solution to HW 2

Home work 2 solutions are as follows: