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Revision 22016-02-19 - TWikiGuest

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Title

The singular value decomposition of a matrix $A$ is defined as

  \begin{displaymath} A = U \Sigma V^H \end{displaymath} (1)
where $U$ and $V$ are both matrices with orthonormal columns, $\{\cdot\}^H$ indicates a complex-conjugate transpose, and $\Sigma$ is a diagonal matrix with singular values
\[ \sigma_1 > \sigma_2 > \cdots > \sigma_n \geq 0 \]
along the main diagonal. Eq. (1) is just one of the many matrix decompositions that exists for matrix $A$.
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Revision 12016-02-16 - TWikiAdminUser

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Title

The singular value decomposition of a matrix $A$ is defined as

  \begin{displaymath} A = U \Sigma V^H \end{displaymath} (2)
where $U$ and $V$ are both matrices with orthonormal columns, $\{\cdot\}^H$ indicates a complex-conjugate transpose, and $\Sigma$ is a diagonal matrix with singular values
\[ \sigma_1 &amp;gt; \sigma_2 &amp;gt; \cdots &amp;gt; \sigma_n \geq 0 \]
along the main diagonal. Eq. (1) is just one of the many matrix decompositions that exists for matrix $A$.

-- TWiki Admin User - 2016-02-16

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