Calculating the Pearson correlation coefficient can be complicated but software makes it much easier. You can use several methods to calculate correlation in Excel.

Stuart R. Lipsitz, Traci Leong, Joseph Ibrahim, Steven Lipshultz, A Partial Correlation Coefficient and Coefficient of Determination for Multivariate Normal Repeated Measures Data, Journal of the ...

The inverse of the correlation matrix, however, also has important interpretations. An exposition of some of the properties connected with the inverse of the correlation matrix is provided and its use ...