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<div class="section" id="torch-det">
<h1>torch.det<a class="headerlink" href="#torch-det" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="torch.det">
<code class="sig-prename descclassname">torch.</code><code class="sig-name descname">det</code><span class="sig-paren">(</span><em class="sig-param">input</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.det" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates determinant of a square matrix or batches of square matrices.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p><a class="reference internal" href="#torch.det" title="torch.det"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.det()</span></code></a> is deprecated. Please use <a class="reference internal" href="../linalg.html#torch.linalg.det" title="torch.linalg.det"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.linalg.det()</span></code></a> instead.</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Backward through <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi><mi>e</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">det</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal">t</span></span></span></span>
</span> internally uses SVD results when <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code> is
not invertible. In this case, double backward through <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi><mi>e</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">det</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal">t</span></span></span></span>
</span> will be
unstable when <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code> doesn’t have distinct singular values. See
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext> </mtext><mi>t</mi><mi>o</mi><mi>r</mi><mi>c</mi><mi>h</mi><mi mathvariant="normal">.</mi><mi>s</mi><mi>v</mi><mi>d</mi></mrow><annotation encoding="application/x-tex">~torch.svd</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mspace nobreak"> </span><span class="mord mathnormal">t</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">c</span><span class="mord mathnormal">h</span><span class="mord">.</span><span class="mord mathnormal">s</span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal">d</span></span></span></span>
</span> for details.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>input</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor of size <code class="docutils literal notranslate"><span class="pre">(*,</span> <span class="pre">n,</span> <span class="pre">n)</span></code> where <code class="docutils literal notranslate"><span class="pre">*</span></code> is zero or more
batch dimensions.</p>
</dd>
</dl>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">A</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">det</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="go">tensor(3.7641)</span>
<span class="gp">>>> </span><span class="n">A</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">A</span>
<span class="go">tensor([[[ 0.9254, -0.6213],</span>
<span class="go"> [-0.5787, 1.6843]],</span>
<span class="go"> [[ 0.3242, -0.9665],</span>
<span class="go"> [ 0.4539, -0.0887]],</span>
<span class="go"> [[ 1.1336, -0.4025],</span>
<span class="go"> [-0.7089, 0.9032]]])</span>
<span class="gp">>>> </span><span class="n">A</span><span class="o">.</span><span class="n">det</span><span class="p">()</span>
<span class="go">tensor([1.1990, 0.4099, 0.7386])</span>
</pre></div>
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