One of the interesting topics in linear algebra is matrix rank. It outlines ways that columns of a matrix correlate to each other. There are basic and free columns. and you can define free columns in terms of linear combination of basic columns. It highlighted a matter of data redundancy to me. So if you can define a column based on other columns, you won't need the content of those columns any more; just keep the coefficients that should be applied to basic columns and you are good to go! It seemed to be highly useful in matrix compression. An image which is a big matrix could be compressed like this by some matter of rank incrementation.
I succeeded in getting an algorithm to alter the rank. Unfortunately as it is not the current topic of my research, I was prohibited to work on this, deviate less and concentrate more on my research area. Anyway I found interesting relevant researches on matrix rank reduction, this is at the back of my mind for sometime to be used.