Statistics Dictionary

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Elementary Operators

Each type of elementary operation may be performed by matrix multiplication, using square matrices called elementary operators.

For example, suppose you want to interchange rows 1 and 2 of Matrix A. To accomplish this, you could premultiply A by E to produce B, as shown below.


0 1
1 0
      
1 3 5
2 4 6
    =    
0 + 2 0 + 4 0 + 6
0 + 1 0 + 3 0 + 5
    =    
2 4 6
1 3 5
E A B

Here, E is an elementary operator. It operates on A to produce the desired interchanged rows in B.

See also:   Elementary Matrix Operations