Issues-with-covaraince-matrix.md

@@ -9,7 +9,7 @@ So far, we were used the simple [`numpy.linalg.inv()`](https://numpy.org/doc/sta
 
 <img src="uploads/5c14e15cf27db9dde43ae57c9da231e0/inv.png"  width="440" ><img src="uploads/5f028dfe024ae56916586e2488a3c602/inv_off_diag.png"  width="440" >
 
-In the above figures, the quantity 'inv' refers to the `numpy.linalg.inv()` function. In the right plot, the quantity 'k' refers to the index of the off-diagonal array;  k>0 for diagonals above the main diagonal, and k<0 for diagonals below the main diagonal. Note that the off-diagonal elements are substantially larger than zero for the left-hand inverse matrix only, and also not consistent with the right-hand inverse matrix.
+In the above figures, the quantity 'inv' refers to the `numpy.linalg.inv()` function. In the right plot, the quantity 'k' refers to the index of the off-diagonal array;  k>0 for diagonals above the main diagonal, and k<0 for diagonals below the main diagonal. Note that the off-diagonal elements are substantially larger than zero for the left-hand inverse matrix only, and also not consistent with the case of right-hand inverse matrix.
 
 To resolve this issue, we propose to use the Moore-Penrose pseudo-inverse method. This method calculates the generalized inverse of a matrix using its singular-value decomposition (SVD) and including all large singular values. We use the numpy inbuild function [`numpy.linalg.pinv()`](https://numpy.org/doc/stable/reference/generated/numpy.linalg.pinv.html). At this moment, let us focus on the above comparison as we showed for the 
 `numpy.linalg.inv()` function.