# [GSoC] Week 9: Matrix Inverse and Sparse Matrices

Hi All, Sorry for a late blog post. I was kind of busy during last week, preparing for a competition.

During the last week, I mainly did two things, implementing matrix inverse and starting the implementation of sparse matrices.

# Implementing Matrix Inverse

I implemented matrix inverse in two different methods, using Gauss Jordan elimination and fraction free LU decomposition. I had only implemented gauss Jordan elimination to solve a system $Ax = b$ where $b$ is a column matrix. I had to enhance the algorithm so that it can be used to solve several systems at once, i.e. $b$ can be a collection of column matrix.

This was not a problem in fraction free LU method because $L$ and $U$ factors can be used to solve column vectors $e_{1}, e_{2}, . . . e_{n}$ after calculating $L$ and $U$ once.

# Implementing Sparse Matrices

We decided to adapt the implementation of SciPy sparse matrices. For the time being I have implemented CSR form of a sparse matrix. CSR is an acronym for “Compress Sparse Row”. You can learn more about it in the following links.

Wiki Article

Netlib Article

You can find information about scipy implementation of CSR matrices here.