Elementary Matrices
Elementary Matrices
Elementary Matrices
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<strong>Elementary</strong> <strong>Matrices</strong><br />
Definition<br />
An n × n matrix is an elementary matrix if it can be obtained<br />
from In by a single elementary row operation.<br />
Example<br />
E is a 2 × 2 elementary matrix formed by swapping the two<br />
rows of I2.<br />
<br />
0<br />
E =<br />
1<br />
<br />
1<br />
0<br />
Note the effect it has upon multiplying an arbitrary matrix.<br />
<br />
0<br />
1<br />
<br />
1 a11<br />
0<br />
a12 a13<br />
<br />
a21<br />
=<br />
a22 a23<br />
<br />
a21 a22 a23<br />
J. Robert Buchanan <strong>Elementary</strong> <strong>Matrices</strong><br />
a11 a12 a13
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