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<title>GAP (MatricesForHomalg) - Appendix A: The Basic Matrix Operations</title>
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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chap6.html">6</a>  <a href="chapA.html">A</a>  <a href="chapB.html">B</a>  <a href="chapC.html">C</a>  <a href="chapD.html">D</a>  <a href="chapE.html">E</a>  <a href="chapF.html">F</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

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<div class="ChapSects"><a href="chapA.html#X7CB422647C7DD289">A <span class="Heading">The Basic Matrix Operations</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA.html#X810454AB85D336F5">A.1 <span class="Heading">Main</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA.html#X8435BB2E7A819478">A.2 <span class="Heading">Effective</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA.html#X7B1023F47EAB7A97">A.3 <span class="Heading">Relative</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA.html#X7A0B865E7E70DB3D">A.4 <span class="Heading">Reduced</span></a>
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<h3>A <span class="Heading">The Basic Matrix Operations</span></h3>

<p>These are the operations used to solve one-sided (in)homogeneous linear systems <span class="SimpleMath">XA=B</span> resp. <span class="SimpleMath">AX=B</span>.</p>

<p><a id="X810454AB85D336F5" name="X810454AB85D336F5"></a></p>

<h4>A.1 <span class="Heading">Main</span></h4>


<ul>
<li><p><code class="func">BasisOfRowModule</code> (<a href="chap5.html#X80ADBE0D82CC6E85"><span class="RefLink">5.5-28</span></a>)</p>

</li>
<li><p><code class="func">BasisOfColumnModule</code> (<a href="chap5.html#X868CDA327D6C8DDC"><span class="RefLink">5.5-29</span></a>)</p>

</li>
</ul>

<ul>
<li><p><code class="func">DecideZeroRows</code> (<a href="chap5.html#X7F851EC7861170D1"><span class="RefLink">5.5-30</span></a>)</p>

</li>
<li><p><code class="func">DecideZeroColumns</code> (<a href="chap5.html#X86C97DBB787BAD6D"><span class="RefLink">5.5-31</span></a>)</p>

</li>
</ul>

<ul>
<li><p><code class="func">SyzygiesGeneratorsOfRows</code> (<a href="chap5.html#X86ECEA9B7A4AE578"><span class="RefLink">5.5-32</span></a>)</p>

</li>
<li><p><code class="func">SyzygiesGeneratorsOfColumns</code> (<a href="chap5.html#X86504B757F6DC990"><span class="RefLink">5.5-33</span></a>)</p>

</li>
</ul>
<p><a id="X8435BB2E7A819478" name="X8435BB2E7A819478"></a></p>

<h4>A.2 <span class="Heading">Effective</span></h4>


<ul>
<li><p><code class="func">BasisOfRowsCoeff</code> (<a href="chap5.html#X7D9DEC6081AF0003"><span class="RefLink">5.5-40</span></a>)</p>

</li>
<li><p><code class="func">BasisOfColumnsCoeff</code> (<a href="chap5.html#X7BBC885F7C24DEC2"><span class="RefLink">5.5-41</span></a>)</p>

</li>
</ul>

<ul>
<li><p><code class="func">DecideZeroRowsEffectively</code> (<a href="chap5.html#X8513963C84A9F8CB"><span class="RefLink">5.5-42</span></a>)</p>

</li>
<li><p><code class="func">DecideZeroColumnsEffectively</code> (<a href="chap5.html#X7A06BF7779830815"><span class="RefLink">5.5-43</span></a>)</p>

</li>
</ul>
<p><a id="X7B1023F47EAB7A97" name="X7B1023F47EAB7A97"></a></p>

<h4>A.3 <span class="Heading">Relative</span></h4>


<ul>
<li><p><code class="func">SyzygiesGeneratorsOfRows</code> (<a href="chap5.html#X84A93458804F16F6"><span class="RefLink">5.5-34</span></a>)</p>

</li>
<li><p><code class="func">SyzygiesGeneratorsOfColumns</code> (<a href="chap5.html#X7D3FC0CE7B63AAF1"><span class="RefLink">5.5-35</span></a>)</p>

</li>
</ul>
<p><a id="X7A0B865E7E70DB3D" name="X7A0B865E7E70DB3D"></a></p>

<h4>A.4 <span class="Heading">Reduced</span></h4>


<ul>
<li><p><code class="func">ReducedBasisOfRowModule</code> (<a href="chap5.html#X82E0FF517DC38040"><span class="RefLink">5.5-36</span></a>)</p>

</li>
<li><p><code class="func">ReducedBasisOfColumnModule</code> (<a href="chap5.html#X84CED11F7A633BDA"><span class="RefLink">5.5-37</span></a>)</p>

</li>
</ul>

<ul>
<li><p><code class="func">ReducedSyzygiesGeneratorsOfRows</code> (<a href="chap5.html#X7DE458D67B9B85BF"><span class="RefLink">5.5-38</span></a>)</p>

</li>
<li><p><code class="func">ReducedSyzygiesGeneratorsOfColumns</code> (<a href="chap5.html#X8699114D7A865C11"><span class="RefLink">5.5-39</span></a>)</p>

</li>
</ul>

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