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<div class="section" id="torch-linalg">
<h1>torch.linalg<a class="headerlink" href="#torch-linalg" title="Permalink to this headline">¶</a></h1>
<p>Common linear algebra operations.</p>
<span class="target" id="module-torch.linalg"></span><div class="section" id="matrix-properties">
<h2>Matrix Properties<a class="headerlink" href="#matrix-properties" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><p id="torch.linalg.norm"/><a class="reference internal" href="generated/torch.linalg.norm.html#torch.linalg.norm" title="torch.linalg.norm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">norm</span></code></a></p></td>
<td><p>Computes a vector or matrix norm.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.linalg.vector_norm"/><a class="reference internal" href="generated/torch.linalg.vector_norm.html#torch.linalg.vector_norm" title="torch.linalg.vector_norm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">vector_norm</span></code></a></p></td>
<td><p>Computes a vector norm.</p></td>
</tr>
<tr class="row-odd"><td><p><p id="torch.linalg.matrix_norm"/><a class="reference internal" href="generated/torch.linalg.matrix_norm.html#torch.linalg.matrix_norm" title="torch.linalg.matrix_norm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">matrix_norm</span></code></a></p></td>
<td><p>Computes a matrix norm.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.linalg.det"/><a class="reference internal" href="generated/torch.linalg.det.html#torch.linalg.det" title="torch.linalg.det"><code class="xref py py-obj docutils literal notranslate"><span class="pre">det</span></code></a></p></td>
<td><p>Computes the determinant of a square matrix.</p></td>
</tr>
<tr class="row-odd"><td><p><p id="torch.linalg.slogdet"/><a class="reference internal" href="generated/torch.linalg.slogdet.html#torch.linalg.slogdet" title="torch.linalg.slogdet"><code class="xref py py-obj docutils literal notranslate"><span class="pre">slogdet</span></code></a></p></td>
<td><p>Computes the sign and natural logarithm of the absolute value of the determinant of a square matrix.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.linalg.cond"/><a class="reference internal" href="generated/torch.linalg.cond.html#torch.linalg.cond" title="torch.linalg.cond"><code class="xref py py-obj docutils literal notranslate"><span class="pre">cond</span></code></a></p></td>
<td><p>Computes the condition number of a matrix with respect to a matrix norm.</p></td>
</tr>
<tr class="row-odd"><td><p><p id="torch.linalg.matrix_rank"/><a class="reference internal" href="generated/torch.linalg.matrix_rank.html#torch.linalg.matrix_rank" title="torch.linalg.matrix_rank"><code class="xref py py-obj docutils literal notranslate"><span class="pre">matrix_rank</span></code></a></p></td>
<td><p>Computes the numerical rank of a matrix.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="decompositions">
<h2>Decompositions<a class="headerlink" href="#decompositions" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><p id="torch.linalg.cholesky"/><a class="reference internal" href="generated/torch.linalg.cholesky.html#torch.linalg.cholesky" title="torch.linalg.cholesky"><code class="xref py py-obj docutils literal notranslate"><span class="pre">cholesky</span></code></a></p></td>
<td><p>Computes the Cholesky decomposition of a complex Hermitian or real symmetric positive-definite matrix.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.linalg.qr"/><a class="reference internal" href="generated/torch.linalg.qr.html#torch.linalg.qr" title="torch.linalg.qr"><code class="xref py py-obj docutils literal notranslate"><span class="pre">qr</span></code></a></p></td>
<td><p>Computes the QR decomposition of a matrix.</p></td>
</tr>
<tr class="row-odd"><td><p><p id="torch.linalg.eig"/><a class="reference internal" href="generated/torch.linalg.eig.html#torch.linalg.eig" title="torch.linalg.eig"><code class="xref py py-obj docutils literal notranslate"><span class="pre">eig</span></code></a></p></td>
<td><p>Computes the eigenvalue decomposition of a square matrix if it exists.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.linalg.eigvals"/><a class="reference internal" href="generated/torch.linalg.eigvals.html#torch.linalg.eigvals" title="torch.linalg.eigvals"><code class="xref py py-obj docutils literal notranslate"><span class="pre">eigvals</span></code></a></p></td>
<td><p>Computes the eigenvalues of a square matrix.</p></td>
</tr>
<tr class="row-odd"><td><p><p id="torch.linalg.eigh"/><a class="reference internal" href="generated/torch.linalg.eigh.html#torch.linalg.eigh" title="torch.linalg.eigh"><code class="xref py py-obj docutils literal notranslate"><span class="pre">eigh</span></code></a></p></td>
<td><p>Computes the eigenvalue decomposition of a complex Hermitian or real symmetric matrix.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.linalg.eigvalsh"/><a class="reference internal" href="generated/torch.linalg.eigvalsh.html#torch.linalg.eigvalsh" title="torch.linalg.eigvalsh"><code class="xref py py-obj docutils literal notranslate"><span class="pre">eigvalsh</span></code></a></p></td>
<td><p>Computes the eigenvalues of a complex Hermitian or real symmetric matrix.</p></td>
</tr>
<tr class="row-odd"><td><p><p id="torch.linalg.svd"/><a class="reference internal" href="generated/torch.linalg.svd.html#torch.linalg.svd" title="torch.linalg.svd"><code class="xref py py-obj docutils literal notranslate"><span class="pre">svd</span></code></a></p></td>
<td><p>Computes the singular value decomposition (SVD) of a matrix.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.linalg.svdvals"/><a class="reference internal" href="generated/torch.linalg.svdvals.html#torch.linalg.svdvals" title="torch.linalg.svdvals"><code class="xref py py-obj docutils literal notranslate"><span class="pre">svdvals</span></code></a></p></td>
<td><p>Computes the singular values of a matrix.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="solvers">
<h2>Solvers<a class="headerlink" href="#solvers" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><p id="torch.linalg.solve"/><a class="reference internal" href="generated/torch.linalg.solve.html#torch.linalg.solve" title="torch.linalg.solve"><code class="xref py py-obj docutils literal notranslate"><span class="pre">solve</span></code></a></p></td>
<td><p>Computes the solution of a square system of linear equations with a unique solution.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.linalg.lstsq"/><a class="reference internal" href="generated/torch.linalg.lstsq.html#torch.linalg.lstsq" title="torch.linalg.lstsq"><code class="xref py py-obj docutils literal notranslate"><span class="pre">lstsq</span></code></a></p></td>
<td><p>Computes a solution to the least squares problem of a system of linear equations.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="inverses">
<h2>Inverses<a class="headerlink" href="#inverses" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><p id="torch.linalg.inv"/><a class="reference internal" href="generated/torch.linalg.inv.html#torch.linalg.inv" title="torch.linalg.inv"><code class="xref py py-obj docutils literal notranslate"><span class="pre">inv</span></code></a></p></td>
<td><p>Computes the inverse of a square matrix if it exists.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.linalg.pinv"/><a class="reference internal" href="generated/torch.linalg.pinv.html#torch.linalg.pinv" title="torch.linalg.pinv"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pinv</span></code></a></p></td>
<td><p>Computes the pseudoinverse (Moore-Penrose inverse) of a matrix.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="matrix-products">
<h2>Matrix Products<a class="headerlink" href="#matrix-products" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><p id="torch.linalg.matrix_power"/><a class="reference internal" href="generated/torch.linalg.matrix_power.html#torch.linalg.matrix_power" title="torch.linalg.matrix_power"><code class="xref py py-obj docutils literal notranslate"><span class="pre">matrix_power</span></code></a></p></td>
<td><p>Computes the <cite>n</cite>-th power of a square matrix for an integer <cite>n</cite>.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.linalg.multi_dot"/><a class="reference internal" href="generated/torch.linalg.multi_dot.html#torch.linalg.multi_dot" title="torch.linalg.multi_dot"><code class="xref py py-obj docutils literal notranslate"><span class="pre">multi_dot</span></code></a></p></td>
<td><p>Efficiently multiplies two or more matrices by reordering the multiplications so that the fewest arithmetic operations are performed.</p></td>
</tr>
<tr class="row-odd"><td><p><p id="torch.linalg.householder_product"/><a class="reference internal" href="generated/torch.linalg.householder_product.html#torch.linalg.householder_product" title="torch.linalg.householder_product"><code class="xref py py-obj docutils literal notranslate"><span class="pre">householder_product</span></code></a></p></td>
<td><p>Computes the first <cite>n</cite> columns of a product of Householder matrices.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="tensor-operations">
<h2>Tensor Operations<a class="headerlink" href="#tensor-operations" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><p id="torch.linalg.tensorinv"/><a class="reference internal" href="generated/torch.linalg.tensorinv.html#torch.linalg.tensorinv" title="torch.linalg.tensorinv"><code class="xref py py-obj docutils literal notranslate"><span class="pre">tensorinv</span></code></a></p></td>
<td><p>Computes the multiplicative inverse of <a class="reference internal" href="generated/torch.tensordot.html#torch.tensordot" title="torch.tensordot"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.tensordot()</span></code></a>.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.linalg.tensorsolve"/><a class="reference internal" href="generated/torch.linalg.tensorsolve.html#torch.linalg.tensorsolve" title="torch.linalg.tensorsolve"><code class="xref py py-obj docutils literal notranslate"><span class="pre">tensorsolve</span></code></a></p></td>
<td><p>Computes the solution <cite>X</cite> to the system <cite>torch.tensordot(A, X) = B</cite>.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="experimental-functions">
<h2>Experimental Functions<a class="headerlink" href="#experimental-functions" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><p id="torch.linalg.cholesky_ex"/><a class="reference internal" href="generated/torch.linalg.cholesky_ex.html#torch.linalg.cholesky_ex" title="torch.linalg.cholesky_ex"><code class="xref py py-obj docutils literal notranslate"><span class="pre">cholesky_ex</span></code></a></p></td>
<td><p>Computes the Cholesky decomposition of a complex Hermitian or real symmetric positive-definite matrix.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.linalg.inv_ex"/><a class="reference internal" href="generated/torch.linalg.inv_ex.html#torch.linalg.inv_ex" title="torch.linalg.inv_ex"><code class="xref py py-obj docutils literal notranslate"><span class="pre">inv_ex</span></code></a></p></td>
<td><p>Computes the inverse of a square matrix if it is invertible.</p></td>
</tr>
</tbody>
</table>
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