Create a block diagonal matrix.

Create a 4-by-4 identity matrix and a 2-by-2 matrix that you want to be repeated along the diagonal.

A = eye(4);
B = [1 -1;-1 1];

Use kron to find the Kronecker tensor product.

K = kron(A,B)

K = 8×8

     1    -1     0     0     0     0     0     0
    -1     1     0     0     0     0     0     0
     0     0     1    -1     0     0     0     0
     0     0    -1     1     0     0     0     0
     0     0     0     0     1    -1     0     0
     0     0     0     0    -1     1     0     0
     0     0     0     0     0     0     1    -1
     0     0     0     0     0     0    -1     1

The result is an 8-by-8 block diagonal matrix.

Expand the size of a matrix by repeating elements.

Create a 2-by-2 matrix of ones and a 2-by-3 matrix whose elements you want to repeat.

A = [1 2 3; 4 5 6];
B = ones(2);

Calculate the Kronecker tensor product using kron.

K = kron(A,B)

K = 4×6

     1     1     2     2     3     3
     1     1     2     2     3     3
     4     4     5     5     6     6
     4     4     5     5     6     6

The result is a 4-by-6 block matrix.

This example visualizes a sparse Laplacian operator matrix.

The matrix representation of the discrete Laplacian operator on a two-dimensional, n-by- n grid is a n*n-by- n*n sparse matrix. There are at most five nonzero elements in each row or column. You can generate the matrix as the Kronecker product of one-dimensional difference operators. In this example n = 5.

n = 5;
I = speye(n,n);
E = sparse(2:n,1:n-1,1,n,n);
D = E+E'-2*I;
A = kron(D,I)+kron(I,D);

Visualize the sparsity pattern with spy.

spy(A,'k')