Specify a band of a matrix
Band[{i, j}]
Band[{imin, jmin, …}, {imax, jmax, …}]
Band[{imin, jmin, …}, {imax, jmax, …}, {di, dj, …}]
SparseArray[{Band[{1, 1}] -> x, Band[{2, 1}] -> y}, {5, 5}]//MatrixForm
→ MatrixForm[SparseArray[Automatic, {5, 5}, 0, {1, {{0, 1, 3, 5, 7, 9}, {{1}, {1}, {2}, {2}, {3}, {3}, {4}, {4}, {5}}}, {x, y, x, y, x, y, x, y, x}}]]SparseArray[Band[{3, 2}] -> x, {5, 5}]//MatrixForm
→ MatrixForm[SparseArray[Automatic, {5, 5}, 0, {1, {{0, 0, 0, 1, 2, 3}, {{2}, {3}, {4}}}, {x, x, x}}]]SparseArray[Band[{1, 1}] -> {x, y, z}, {5, 5}]//MatrixForm
→ MatrixForm[SparseArray[Automatic, {5, 5}, 0, {1, {{0, 1, 2, 3, 4, 5}, {{1}, {2}, {3}, {4}, {5}}}, {{x, y, z}, {x, y, z}, {x, y, z}, {x, y, z}, {x, y, z}}}]]