Sir, 

I found from issue 10701 <https://github.com/sympy/sympy/issues/10701> that 
using is_nilpotent() function for checking whether a matrix is nil potent 
or not is giving error for empty matrices. So what I have found and thought 
are commented there in the issue itself. So as suggested by argriffing(git 
hub name, I don't know his original name :P ), I would like to discuss with 
sympy devs about this issue. During this work I also have found that the 
same error being given when tried to use eigenvals() and eigenvects() for 
finding eigen values and eigen vectors respectively for an empty matrix. I 
have some ideas here for which I need some guidance from the devs.

1) To return an empty dict as result for *eigenvals()* when it is applied 
on an empty matrix. 
2) For *eigenvects()*, to return an empty list for an empty matrix.
3) And for *is_nilpotent()*, to return False for which I have mentioned 
some reasons there on the link provided. 

For all these ideas I have mentioned, to implement them, we have to check 
that the given matrix is an empty matrix to do some extra work for that. 
And to do that easily, I think we need a routine which takes a matrix as 
input, returns *True* if it is empty, returns F*alse* if it isn't. 

So please anyone look into this and please provide your valuable inputs to 
correct me or even make the statement more clear and standard. 

Thank you, 
Aravind

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