2.42 Generate sparse matrix with n by n matrix repeated on its diagonal

Given matrix \(\begin {pmatrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end {pmatrix} \), generate the following sparse matrix with this matrix on the diagonal

\[\begin {pmatrix} 1 & 2 & 3 & 0 & 0 & 0 & 0 & 0 & 0\\ 4 & 5 & 6 & 0 & 0 & 0 & 0 & 0 & 0\\ 7 & 8 & 9 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 & 2 & 3 & 0 & 0 & 0\\ 0 & 0 & 0 & 4 & 5 & 6 & 0 & 0 & 0\\ 0 & 0 & 0 & 7 & 8 & 9 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 3\\ 0 & 0 & 0 & 0 & 0 & 0 & 4 & 5 & 6\\ 0 & 0 & 0 & 0 & 0 & 0 & 7 & 8 & 9 \end {pmatrix} \]

Mathematica mat = N[{{1,2,3},{4,5,6},{7,8,9}}]; sp = SparseArray[Band[{1,1}]-> ConstantArray[mat,{3}]] MatrixForm[sp]

\[ \left ( {\begin {array}{ccccccccc} 1. & 2. & 3. & 0 & 0 & 0 & 0 & 0 & 0 \\ 4. & 5. & 6. & 0 & 0 & 0 & 0 & 0 & 0 \\ 7. & 8. & 9. & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1. & 2. & 3. & 0 & 0 & 0 \\ 0 & 0 & 0 & 4. & 5. & 6. & 0 & 0 & 0 \\ 0 & 0 & 0 & 7. & 8. & 9. & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1. & 2. & 3. \\ 0 & 0 & 0 & 0 & 0 & 0 & 4. & 5. & 6. \\ 0 & 0 & 0 & 0 & 0 & 0 & 7. & 8. & 9. \\ \end {array}} \right ) \]

 

Matlab A = [1 2 3; 4 5 6; 7 8 9]; Iy = speye(3); full(Iy)	ans = 1 0 0 0 1 0 0 0 1
sp = kron(Iy,A); full(sp)	ans = 1 2 3 0 0 0 0 0 0 4 5 6 0 0 0 0 0 0 7 8 9 0 0 0 0 0 0 0 0 0 1 2 3 0 0 0 0 0 0 4 5 6 0 0 0 0 0 0 7 8 9 0 0 0 0 0 0 0 0 0 1 2 3 0 0 0 0 0 0 4 5 6 0 0 0 0 0 0 7 8 9

 

Maple A:=Matrix([[1,2,3],[4,5,6],[7,8,9]]); Iy:=LinearAlgebra:-IdentityMatrix(3); LinearAlgebra:-KroneckerProduct(Iy,A)

Matrix(9, 9, [[1, 2, 3, 0, 0, 0, 0, 0, 0], [4, 5, 6, 0, 0, 0, 0, 0, 0], [7, 8, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 3, 0, 0, 0], [0, 0, 0, 4, 5, 6, 0, 0, 0], [0, 0, 0, 7, 8, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 2, 3], [0, 0, 0, 0, 0, 0, 4, 5, 6], [0, 0, 0, 0, 0, 0, 7, 8, 9]])