The attached PDF is the annotated draft from my Professor. The Doc file is the original draft which you will need to work on and then send the revised version to me. I will give tips for quality work.

This revision work in my opinion is easy since there are only few parts of the paper need to be fixed.

Here is the email from my Professor.

I have attached the annotated draft. Here are my comments:

– There are some issues with line spacing.

– You repeated yourself a bit on the first page.

– I am happy that you added more connecting phrases between the sections.

– In the section on matrices you state that alpha = a+bi+cj+dk andalpha = aU+bI+cJ+dK. I don’t think you mean that these are literallyequal. I think you mean that there is a function f that sends aquaternion alpha to a matrix f(alpha). You should alsomention that this function preserves addition and multiplication:f(alpha+beta)=f(alpha)+f(beta) and f(alpha*beta)=f(alpha)*f(beta). Ifthese formulas are not true then the representation would make no sense.

– You say to “recall” that for an imaginary quaternion v we haveexp(v)= cos|v|+(v/|v|) sin|v|, but where are we supposed to recall thisfrom? You didn’t prove it. To prove it, first define u=v/|v|, so thatu^2=-1. Then we also have u^2=-1, u^3=-u, u^4=1,u^5=u, etc. Now plug v=u|v| into into the power series definition of theexponential and observe that

exp(v) = exp(u|v|) = sum_{k>=0} 1/k! u^k|v|^k = (power series for cos|v|) + u (power series for |v|).

Please make sure that all the anotations in red need to be revised! So do the points listed in the email above.