Issues-with-covaraince-matrix.md

@@ -3,4 +3,7 @@ We use the inverse of the covariance matrix to compute the weighted inner produc
 ```math
 \Sigma^{-1} \: \Sigma =  \Sigma \: \Sigma^{-1} = I
 ```
+Thus, the diagonal elements of the above inner product must be equal to 1 (or nearly equal to 1 for numerical computation) and off-diagonal elements must be zero (or nearly equal to zero). The inner product should be invariant for the choice of whether the right-hand inverse matrix or left-hand inverse matrix.
 
+So far, we were used the simple [`numpy.linalg.inv()`](https://numpy.org/doc/stable/reference/generated/numpy.linalg.inv.html) function to calculate the inverse of a matrix. In this case, we found a disagreement between right-hand inverse matrix or left-hand inverse matrix. 
+![inv](uploads/c077dbc52b6d9b13080492c543f15736/inv.png)