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364 lines
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364 lines
15 KiB
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<a href="../MathNet.Numerics.Providers.SparseSolver/index.htm">MathNet.Numerics.Providers.SparseSolver</a>
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<a href="../MathNet.Numerics.Random/index.htm">MathNet.Numerics.Random</a>
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</ul>
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</div>
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</div><div id="types">
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<h2 class="fixed">Types in MathNet.Numerics.LinearAlgebra.Factorization</h2>
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<div class="scroll">
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<ul>
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<li>
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<a href="../MathNet.Numerics.LinearAlgebra.Factorization/Cholesky`1.htm">Cholesky<T></a>
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</li>
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<li>
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<a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm" class="current">Evd<T></a>
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</li>
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<li>
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<a href="../MathNet.Numerics.LinearAlgebra.Factorization/GramSchmidt`1.htm">GramSchmidt<T></a>
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</li>
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<li>
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<a href="../MathNet.Numerics.LinearAlgebra.Factorization/ISolver`1.htm">ISolver<T></a>
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</li>
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<li>
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<a href="../MathNet.Numerics.LinearAlgebra.Factorization/LU`1.htm">LU<T></a>
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</li>
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<li>
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<a href="../MathNet.Numerics.LinearAlgebra.Factorization/QR`1.htm">QR<T></a>
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</li>
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<li>
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<a href="../MathNet.Numerics.LinearAlgebra.Factorization/QRMethod.htm">QRMethod</a>
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</li>
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<li>
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<a href="../MathNet.Numerics.LinearAlgebra.Factorization/Svd`1.htm">Svd<T></a>
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</li>
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</ul>
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</div>
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</div>
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<div class="header">
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<p class="class"><strong>Type</strong> Evd<T></p>
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<p><strong>Namespace</strong> MathNet.Numerics.LinearAlgebra.Factorization</p>
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<p><strong>Interfaces</strong> <a href="../MathNet.Numerics.LinearAlgebra.Factorization/ISolver`1.htm">ISolver<T></a></p>
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</div>
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<div class="sub-header">
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<div id="summary">Eigenvalues and eigenvectors of a real matrix. <blockquote class="remarks">
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If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
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diagonal and the eigenvector matrix V is orthogonal.
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I.e. A = V*D*V' and V*VT=I.
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If A is not symmetric, then the eigenvalue matrix D is block diagonal
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with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
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lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The
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columns of V represent the eigenvectors in the sense that A*V = V*D,
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i.e. A.Multiply(V) equals V.Multiply(D). The matrix V may be badly
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conditioned, or even singular, so the validity of the equation
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A = V*D*Inverse(V) depends upon V.Condition().
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</blockquote>
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</div>
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<h3 class="section">Methods</h3>
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<ul>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#Equals">Equals</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#GetHashCode">GetHashCode</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#GetType">GetType</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#Solve">Solve</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#Solve">Solve</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#Solve">Solve</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#Solve">Solve</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#ToString">ToString</a></li>
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</ul>
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<h3 class="section">Properties</h3>
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<ul>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#D">D</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#Determinant">Determinant</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#EigenValues">EigenValues</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#EigenVectors">EigenVectors</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#IsFullRank">IsFullRank</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#IsSymmetric">IsSymmetric</a></li>
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<li><a href="../MathNet.Numerics.LinearAlgebra.Factorization/Evd`1.htm#Rank">Rank</a></li>
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</ul>
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</div>
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<h3 class="section">Public Methods</h3>
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<div id="Equals" class="method">
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<h4><span title="System.bool">bool</span> <strong>Equals</strong>(<span title="System.object">object</span> obj)</h4>
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<div class="content">
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</div>
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</div>
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<div id="GetHashCode" class="method">
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<h4><span title="System.int">int</span> <strong>GetHashCode</strong>()</h4>
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<div class="content">
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</div>
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</div>
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<div id="GetType" class="method">
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<h4><span title="System.Type">Type</span> <strong>GetType</strong>()</h4>
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<div class="content">
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</div>
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</div>
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<div id="Solve" class="method">
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<h4><a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix<T></a> <strong>Solve</strong>(<a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix<T></a> input)</h4>
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<div class="content">Solves a system of linear equations, , with A EVD factorized.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix<T></a></code> input</h6>
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<p class="comments">The right hand side <a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix`1</a> , . </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix<T></a></code></h6>
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<p>The left hand side <a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix`1</a> , . </p>
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</div>
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</div>
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</div>
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<div id="Solve" class="method">
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<h4><span title="System.void">void</span> <strong>Solve</strong>(<a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix<T></a> input, <a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix<T></a> result)</h4>
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<div class="content">Solves a system of linear equations, , with A EVD factorized.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix<T></a></code> input</h6>
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<p class="comments">The right hand side <a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix`1</a> , . </p>
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<h6><code><a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix<T></a></code> result</h6>
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<p class="comments">The left hand side <a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix`1</a> , . </p>
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</div>
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</div>
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</div>
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<div id="Solve" class="method">
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<h4><a href="../MathNet.Numerics.LinearAlgebra/Vector`1.htm">Vector<T></a> <strong>Solve</strong>(<a href="../MathNet.Numerics.LinearAlgebra/Vector`1.htm">Vector<T></a> input)</h4>
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<div class="content">Solves a system of linear equations, , with A EVD factorized.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><a href="../MathNet.Numerics.LinearAlgebra/Vector`1.htm">Vector<T></a></code> input</h6>
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<p class="comments">The right hand side vector, . </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><a href="../MathNet.Numerics.LinearAlgebra/Vector`1.htm">Vector<T></a></code></h6>
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<p>The left hand side <a href="../MathNet.Numerics.LinearAlgebra/Vector`1.htm">Vector`1</a> , . </p>
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</div>
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</div>
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</div>
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<div id="Solve" class="method">
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<h4><span title="System.void">void</span> <strong>Solve</strong>(<a href="../MathNet.Numerics.LinearAlgebra/Vector`1.htm">Vector<T></a> input, <a href="../MathNet.Numerics.LinearAlgebra/Vector`1.htm">Vector<T></a> result)</h4>
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<div class="content">Solves a system of linear equations, , with A EVD factorized.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><a href="../MathNet.Numerics.LinearAlgebra/Vector`1.htm">Vector<T></a></code> input</h6>
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<p class="comments">The right hand side vector, . </p>
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<h6><code><a href="../MathNet.Numerics.LinearAlgebra/Vector`1.htm">Vector<T></a></code> result</h6>
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<p class="comments">The left hand side <a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix`1</a> , . </p>
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</div>
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</div>
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</div>
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<div id="ToString" class="method">
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<h4><span title="System.string">string</span> <strong>ToString</strong>()</h4>
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<div class="content">
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</div>
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</div>
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<h3 class="section">Public Properties</h3>
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<div id="D" class="method">
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<h4><a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix<T></a> <strong>D</strong> get; </h4>
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<div class="content">Gets or sets the block diagonal eigenvalue matrix.
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</div>
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</div>
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<div id="Determinant" class="method">
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<h4><span title="MathNet.Numerics.LinearAlgebra.Factorization.T">T</span> <strong>Determinant</strong> get; </h4>
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<div class="content">Gets the absolute value of determinant of the square matrix for which the EVD was computed.
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</div>
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</div>
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<div id="EigenValues" class="method">
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<h4><a href="../MathNet.Numerics.LinearAlgebra/Vector`1.htm">Vector<T></a> <strong>EigenValues</strong> get; </h4>
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<div class="content">Gets or sets the eigen values (λ) of matrix in ascending value.
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</div>
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</div>
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<div id="EigenVectors" class="method">
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<h4><a href="../MathNet.Numerics.LinearAlgebra/Matrix`1.htm">Matrix<T></a> <strong>EigenVectors</strong> get; </h4>
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<div class="content">Gets or sets eigenvectors.
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</div>
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</div>
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<div id="IsFullRank" class="method">
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<h4><span title="System.bool">bool</span> <strong>IsFullRank</strong> get; </h4>
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<div class="content">Gets a value indicating whether the matrix is full rank or not.
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<blockquote class="value">
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<strong>Value: </strong>
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</blockquote>
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</div>
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</div>
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<div id="IsSymmetric" class="method">
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<h4><span title="System.bool">bool</span> <strong>IsSymmetric</strong> get; </h4>
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<div class="content">Gets or sets a value indicating whether matrix is symmetric or not
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</div>
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</div>
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<div id="Rank" class="method">
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<h4><span title="System.int">int</span> <strong>Rank</strong> get; </h4>
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<div class="content">Gets the effective numerical matrix rank.
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<blockquote class="value">
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<strong>Value: </strong>
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</blockquote>
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</div>
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</div>
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<div id="footer">
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<p>Based on v5.0.0.0 of MathNet.Numerics (Math.NET Numerics)</p>
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<p>Generated by <a href="http://docu.jagregory.com">docu</a></p>
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