Page 142 - 35Linear Algebra

142 Matrices

Notice how the endproducts of MN and NM are different, so MN 6= NM here.

7.3.2 Block Matrices

It is often convenient to partition a matrix M into smaller matrices called
blocks. For example

 
1 2 3 1

4 5 6 0 A B
 
M =   =
7 8 9 1 C D
 
0 1 2 0
   
1 2 3 1

Where A =  4 5 6 , B =  
0 , C = 0 1 2 , D = (0).

7 8 9 1
• The blocks of a block matrix must fit together to form a rectangle. So

B A C B
makes sense, but does not.
D C D A

Reading homework: problem 4

• There are many ways to cut up an n × n matrix into blocks. Often
context or the entries of the matrix will suggest a useful way to divide
the matrix into blocks. For example, if there are large blocks of zeros
in a matrix, or blocks that look like an identity matrix, it can be useful
to partition the matrix accordingly.

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