You can find a good one here. Note that at first he describes the process geometrically for a 2 dimension data set, and then jumps to matrices when he describes the hypothetical 128 electrode EEG data set. This is why we use matrices–to conduct data analysis in dimensions that we cannot easily visualize or chart. ICA is the useful process of removing artifacts from the data, and it generally relies on the fact that these artifacts are linearly independent of one another. Even when the sources are not linearly independent, the analysis will find a place where they are the most independent of one another. Most of his explanation relies upon MATLAB, the student version of which you can find here.
Introduction to independent component analysis
October 21, 2008 by Andy