The reason that the diagonal of the inverse covariance matrix is interesting is that it tells you the rough size of an ellipsoid that will contain your data. T

The reason that the diagonal of the inverse covariance matrix is interesting is that it tells you the rough size of an ellipsoid that will contain your data. That is, if you have a data table of floating point measurements with N columns and M rows, and you interpret each row as a vector in N-space, you want to know roughly how much scatter there is of the M points in N-space. The dimensions of the covariance ellipsoid give you a good first cut at this (assuming that deviations aren't too large). (Google results for "covariance ellipsoid" are surprisingly bad. This book result is ok though: http://books.google.com/books?id=XphcKk7VBqUC&pg=PA116&dq=covariance+ellipsoid http://books.google.com/books?id=XphcKk7VBqUC&pg=PA116&#...)