Hi!

My name is Aditya Chetan, I am a first-year undergrad at Indraprastha 
Institute of information Technology, New Delhi, enrolled in the Computer 
Science and Applied Mathematics program. I got introduced to SymPy a couple 
of weeks back and being an ardent lover of mathematics, have enjoyed toying 
around with the library since then. Having taken a course in Linear Algebra 
at college, I particularly enjoyed the wide range of functionality that the 
module provides for processing vectors and representing them. From the 
Gram-Schmidt process to calculating the diagonalized form of a matrix, I 
enjoyed my time playing around with it. 

However, I noticed that there is no implementation of abstract concepts of 
Linear Algebra such as Vector spaces, Subspaces, and Fields. I would be 
interested in working on a module that implements these concepts as well as 
other concepts of Linear Algebra. This module will be dedicated to Linear 
Algebra and would be responsible for implementation of basic operations on 
Vector objects.

I would also like to work on improving the deficiencies in the existing 
Matrices module that have been listed on the Linear-Algebra-vision 
<https://github.com/sympy/sympy/wiki/Linear-Algebra-Vision> page.

Speaking of my skills, I have completed a university-level course in Python 
and have also taken various online courses in the language. Hence, I am 
quite comfortable with the syntax. As for the Maths portion, I have 
completed a course in Linear Algebra in college. As for my skills as a 
developer, I am a newcomer but would love to work on this idea that I have 
mentioned above. I have studied the various functionalities provided by 
SymPy in the past two weeks and love it as a tool, and am excited to work 
more on it. However, I am a bit unsure about the time it will take to make 
this module and implementing how many functions will be feasible during the 
GSoC period. 

Hence, I need a bit of help in breaking down my goals into sub-tasks ( 
especially printing in different environments, code generation, 
interoperability with other libraries ) and while taking care that my 
project fits into the existing module and its feasibility as a GSoC idea.

Regards,
Aditya Chetan

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