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<p><font face="serif">So some of you are working on the jacoby
portion of the NMR problem and running up against the problem of
how to calculate norms of vectors of complex numbers. There are
two ways that I have used in the past.</font></p>
<p><font face="serif">Method 1:</font></p>
<p><font face="serif"><math
xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mo>=</mo><msqrt><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><mrow><mo
stretchy="false">|</mo><msub><mi>C</mi><mi>i</mi></msub><msup><mo
stretchy="false">|</mo><mn>2</mn></msup></mrow></mrow></msqrt></mrow><annotation
encoding="TeX">norm=\sqrt{\sum_{i=1}^N{ |C_i|^2}}</annotation></semantics></math>Method
2:</font></p>
<p><font face="serif"><math
xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mo>=</mo><msqrt><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>C</mi><mi>i</mi></msub><msubsup><mi>C</mi><mi>i</mi><mo>*</mo></msubsup></mrow></msqrt></mrow><annotation
encoding="TeX">norm = \sqrt{\sum_{i=1}^N C_i C^*_i }</annotation></semantics></math><br>
</font></p>
<p><font face="serif">where the asterisk indicates the complex
conjugate of the entry. The norm itself should not be a complex
number.</font></p>
<p><font face="serif"><br>
</font></p>
<div class="moz-signature">-- <br>
<b><i>Andrew J. Pounds, Ph.D.</i></b><br>
<i>Professor of Chemistry and Computer Science</i><br>
<i>Director of the Computational Science Program</i><br>
<i>Mercer University, Macon, GA 31207 (478) 301-5627</i></div>
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