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<h1 class="chapter"> 45. cholesky </h1>
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<tr><td align="left" valign="top"><a href="#SEC174">45.1 Definitions for cholesky</a></td><td> </td><td align="left" valign="top">
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<h2 class="section"> 45.1 Definitions for cholesky </h2>
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<dt><u>Function:</u> <b>cholesky</b><i> (<var>A</var>)</i>
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<a name="IDX1387"></a>
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<dd><p>Compute Cholesky decomposition of <var>A</var>,
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a lower-triangular matrix <var>L</var> such that <code>L . transpose(L) = A</code>.
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<p>Some examples follow.
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</p><table><tr><td> </td><td><pre class="example">(%i1) load("cholesky")$
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(%i2) A : matrix ([a, b, c], [d, e, f], [g, h, i]);
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(%i3) A2 : transpose (A) . A;
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[ g + d + a g h + d e + a b g i + d f + a c ]
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[ g h + d e + a b h + e + b h i + e f + b c ]
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[ g i + d f + a c h i + e f + b c i + f + c ]
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(%i4) B : cholesky (A2)$
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(%i5) B . transpose (B) - A2;
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</pre></td></tr></table>
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</p><table><tr><td> </td><td><pre class="example">(%i6) A : matrix ([2, 3, 4], [-2, 2,- 3], [11, -2, 3]);
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(%i7) A2 : transpose (A) . A;
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(%i8) B : cholesky (A2);
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[ - --------- ---------- 0 ]
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(%o8) [ sqrt(129) sqrt(129) ]
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[ 47 940 sqrt(129) 153 ]
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[ --------- -------------- ---------- ]
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[ sqrt(129) 129 sqrt(1793) sqrt(1793) ]
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(%i9) B . transpose (B) - A2;
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</pre></td></tr></table>
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<p>To use this function write first <code>load("cholesky")</code>.
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