Language Reference

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. Empty matrices are supported, but have no effect. The matrices are combined diagonally to form a new matrix.

For example, if $\bA $, $\bB $, and $\bC $ 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 25.56: 

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

Figure 25.56: 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