Ideas for contributing to SymPy's linear algebra capabiliites

[Narendra Aironi]

Hey,

I find the SymPy library a great open-source resource for symbolic mathematics, having used it extensively during my undergrad course. I would now like to contribute, specifically, in the 'sympy.matrices' submodule, as my expertise lies mostly in linear algebra and vector calculus. 

On this link, I found relevant ideas list but needed information on what progress has been made --

• Refactor the MatrixBase class.
• Add more special matrices to the matrix expressions module, and migrate some special matrices from the quantum physics module.
• Add more matrix decomposition methods: Schur Decomposition, Polar Decomposition, Hermite Decomposition, ...
• Make the matrices use the specialized data types (Modular Integers, Gaussian Rationals, Polynomial Ring, ...) from the polys module.

Also, if there are any topics in linear algebra, the maintainers would like to see in SymPy, even a vague concept or design pattern, I would love to start ideating on it. If I can implement that idea in small measure, I could then apply for GSoC to contribute rigorously and full-time for a few months. Hoping to see some ambitious, prospective ideas.

Regards,

Narendra