BLOCK Function

BLOCK (matrix1 <, matrix2, …, matrix15> ) ;

The BLOCK function forms a block-diagonal matrix. The blocks are defined by the arguments to the function. Up to 15 matrices can be specified. The matrices are combined diagonally to form a new matrix.

For example, if $\mb {A}$, $\mb {B}$, and $\mb {C}$ are any matrices, then the block matrix formed from these matrices has the following form:

\[  \left[ \begin{array}{ccc} A &  0 &  0 \\ 0 &  B &  0 \\ 0 &  0 &  C \end{array} \right]  \]

The following statements produce a block-diagonal matrix composed of three blocks, shown in Figure 23.51:

a = 1;
b = {2 2,
     3 3};
c = {4 4 4,
     5 5 5};
d = block(a, b, c);
print d;

Figure 23.51: Block Matrix

d
1 0 0 0 0 0
0 2 2 0 0 0
0 3 3 0 0 0
0 0 0 4 4 4
0 0 0 5 5 5