Improve logm , sqrtm and funm - GSoC 2017

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Improve logm , sqrtm and funm - GSoC 2017


I have been following this project and I need to know few things about the proposed project.

Project description says implementing some of the missing MATLAB functions related to matrix functions.

Although logm , sqrtm and expm are already implemented.

So are we talking about improving the efficiency or improving the functions to include "defective matrices"?
(link posted on project talks about "defective matrices".

And which functions are we considering in funm implementation?

Some of the references I'm using are:
Kindly, help me out with my concerns and guide me in a righteous path.