I have a 15*15 banded symmetric matrix, whose inverse is to be done using symbolic math. If there is any proof that for inverse of a symmetric matrix with fixed bandwidth, elements that were zero in original matrix will remain zero in inverse also?
There are plenty of discussions and papers on the web devoted to the topic. Here are a few links:
1. http://www.sciencedirect.com/science/article/pii/S0377042712003081
2. http://math.stackexchange.com/questions/179893/how-to-invert-a-very-regular-banded-toeplitz-matrix
3. http://www-math.mit.edu/~gs/papers/Paper5_ver7.pdf
4. http://faculty.nps.edu/pstanica/research/2013JCAM_BandedMatr.pdf
5. http://arxiv.org/pdf/1002.4545.pdf?origin=publication_detail
6. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.7659
7. http://users.ece.cmu.edu/~moura/papers/t-sp-feb05-asifmoura-ieeexplore.pdf
8. http://www.emeraldinsight.com/journals.htm?articleid=878056
Good luck!
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