Slides from 18th Conference of the International Linear Algebra Society (ILAS), held in Providence, Rhode Island, USA on June 3-7, 2013. These slides augment the paper: Shani Jose and K. C. Sivakumar. On inverse-positivity of sub-direct sums of matrices. Linear Algebra and its Applications, Volume 439, Number 6, pp. 1670-1677, 2013.