Discussion. Differences along a line of sites [fdip-00AE]
Discussion. Differences along a line of sites [fdip-00AE]
On a line of sites the difference \(\varphi (x+1)-\varphi (x)\) is a linear function of the values of \(\varphi \). Written as a matrix, with one row for each step and one column for each site, it is the familiar bidiagonal matrix with \(-1\) and \(1\) in each row. The second difference on the sites is the transpose of that matrix multiplied by the matrix. The same array can be written for any finite carrier once an order of the sites and of the steps is chosen.