Hey, my name is Kartik Sethi. I am interested in taking part in Gsoc this 
year. I have been contributing to sympy for the past couple of months.

I have come up with a few ideas for Gsoc. I am focusing primarily on the 
sympy matrices module.


   1. Implementing complete Singular Value decomposition. Sympy currently 
   has a function for condensed SVD ( I am a contributor on this #20761 
   <https://github.com/sympy/sympy/pull/20761>). 
   2. Using the complete SVD, I can implement Polar decomposition
   3. Hermite Normal Form. There is an old un-merged PR (#18534 
   <https://github.com/sympy/sympy/pull/18534>), I could work on this and 
   complete it.
   4. Sparse-Fraction Free Algorithm another old unfinished PR (#9133 
   <https://github.com/sympy/sympy/pull/9133>)
   5. Jordan Canonical Form
   6. Improve time complexity for QR decomposition of upper Hessenberg. 
   There is an algorithm using Householder reflectors that can cut down 
   time-complexity to O(n^2) instead of current O(n^3)

I am open to adding to this list with the help of possible mentors. I have 
taken a course in Matrix Computations in my previous semester, so I think I 
can really help improve and add to the matrices module.

Thank You
Github id- ks147 <https://github.com/ks147>

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