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EigenvalueDecomposition
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Jama</FONT>
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Class EigenvalueDecomposition</H2>
<PRE>
java.lang.Object
<IMG SRC="../resources/inherit.gif" ALT="extended by "><B>Jama.EigenvalueDecomposition</B>
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<DL>
<DT><B>All Implemented Interfaces:</B> <DD>java.io.Serializable</DD>
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<DT><PRE>public class <B>EigenvalueDecomposition</B><DT>extends java.lang.Object<DT>implements java.io.Serializable</DL>
</PRE>
<P>
Eigenvalues and eigenvectors of a real matrix.
<P>
If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
diagonal and the eigenvector matrix V is orthogonal.
I.e. A = V.times(D.times(V.transpose())) and
V.times(V.transpose()) equals the identity matrix.
<P>
If A is not symmetric, then the eigenvalue matrix D is block diagonal
with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The
columns of V represent the eigenvectors in the sense that A*V = V*D,
i.e. A.times(V) equals V.times(D). The matrix V may be badly
conditioned, or even singular, so the validity of the equation
A = V*D*inverse(V) depends upon V.cond().
<P>
<P>
<DL>
<DT><B>See Also:</B><DD><A HREF="../serialized-form.html#Jama.EigenvalueDecomposition">Serialized Form</A></DL>
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<TD><CODE><B><A HREF="../Jama/EigenvalueDecomposition.html#EigenvalueDecomposition(Jama.Matrix)">EigenvalueDecomposition</A></B>(<A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A> Arg)</CODE>
<BR>
Check for symmetry, then construct the eigenvalue decomposition</TD>
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<CODE> <A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../Jama/EigenvalueDecomposition.html#getD()">getD</A></B>()</CODE>
<BR>
Return the block diagonal eigenvalue matrix</TD>
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<CODE> double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../Jama/EigenvalueDecomposition.html#getImagEigenvalues()">getImagEigenvalues</A></B>()</CODE>
<BR>
Return the imaginary parts of the eigenvalues</TD>
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<CODE> double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../Jama/EigenvalueDecomposition.html#getRealEigenvalues()">getRealEigenvalues</A></B>()</CODE>
<BR>
Return the real parts of the eigenvalues</TD>
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<CODE> <A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../Jama/EigenvalueDecomposition.html#getV()">getV</A></B>()</CODE>
<BR>
Return the eigenvector matrix</TD>
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<A NAME="EigenvalueDecomposition(Jama.Matrix)"><!-- --></A><H3>
EigenvalueDecomposition</H3>
<PRE>
public <B>EigenvalueDecomposition</B>(<A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A> Arg)</PRE>
<DL>
<DD>Check for symmetry, then construct the eigenvalue decomposition
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>A</CODE> - Square matrix</DL>
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<A NAME="getV()"><!-- --></A><H3>
getV</H3>
<PRE>
public <A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A> <B>getV</B>()</PRE>
<DL>
<DD>Return the eigenvector matrix
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>V</DL>
</DD>
</DL>
<HR>
<A NAME="getRealEigenvalues()"><!-- --></A><H3>
getRealEigenvalues</H3>
<PRE>
public double[] <B>getRealEigenvalues</B>()</PRE>
<DL>
<DD>Return the real parts of the eigenvalues
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>real(diag(D))</DL>
</DD>
</DL>
<HR>
<A NAME="getImagEigenvalues()"><!-- --></A><H3>
getImagEigenvalues</H3>
<PRE>
public double[] <B>getImagEigenvalues</B>()</PRE>
<DL>
<DD>Return the imaginary parts of the eigenvalues
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>imag(diag(D))</DL>
</DD>
</DL>
<HR>
<A NAME="getD()"><!-- --></A><H3>
getD</H3>
<PRE>
public <A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A> <B>getD</B>()</PRE>
<DL>
<DD>Return the block diagonal eigenvalue matrix
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>D</DL>
</DD>
</DL>
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