In the above figures, the quantity 'inv' refers to the `numpy.linalg.inv()` function. 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.
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 right-hand inverse matrix only, but the off-diagonal elements are nearly equal to zero for left-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).
