I understand that the outer product of two vectors, say representing two detrended time series, can represent a cross-correlation (well covariance) matrix.
I also know that the inverse of a correlation matrix represents the partial correlations between two variables. Geometrically, I know that the partial correlation between two variables is the angle formed by the projection of their residuals when regressed against all other variables onto the surface perpendicular to all other variables.
I'm wondering how these two relate. That is, I know the interpretation of the inverse of matrix (partial correlation) but not the matrix or its construction.