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<h2 class="chapter">5 Matrix Factorizations</h2>

<p><a name="index-matrix-factorizations-624"></a><a name="index-factorizations-625"></a>

<div class="defun">
&mdash; :  <b>AEPBALANCE</b> (<var>void</var>)<var><a name="index-AEPBALANCE-626"></a></var><br>
&mdash; :  <b>AEPBALANCE</b> (<var>const Matrix &amp;a, const char *balance_job</var>)<var><a name="index-AEPBALANCE-627"></a></var><br>
&mdash; :  <b>AEPBALANCE</b> (<var>const AEPBALANCE &amp;a</var>)<var><a name="index-AEPBALANCE-628"></a></var><br>
        </div>

<div class="defun">
&mdash; : AEPBALANCE&amp; <b>operator =</b> (<var>const AEPBALANCE &amp;a</var>)<var><a name="index-operator-_003d-629"></a></var><br>
        </div>

<div class="defun">
&mdash; : Matrix <b>balanced_matrix</b> (<var>void</var>)<var> const<a name="index-balanced_005fmatrix-630"></a></var><br>
&mdash; : Matrix <b>balancing_matrix</b> (<var>void</var>)<var> const<a name="index-balancing_005fmatrix-631"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const AEPBALANCE &amp;a</var>)<var><a name="index-operator-_003c_003c-632"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>ComplexAEPBALANCE</b> (<var>void</var>)<var><a name="index-ComplexAEPBALANCE-633"></a></var><br>
&mdash; :  <b>ComplexAEPBALANCE</b> (<var>const ComplexMatrix &amp;a, const char *balance_job</var>)<var><a name="index-ComplexAEPBALANCE-634"></a></var><br>
&mdash; :  <b>ComplexAEPBALANCE</b> (<var>const ComplexAEPBALANCE &amp;a</var>)<var><a name="index-ComplexAEPBALANCE-635"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexAEPBALANCE&amp; <b>operator =</b> (<var>const ComplexAEPBALANCE &amp;a</var>)<var><a name="index-operator-_003d-636"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexMatrix <b>balanced_matrix</b> (<var>void</var>)<var> const<a name="index-balanced_005fmatrix-637"></a></var><br>
&mdash; : ComplexMatrix <b>balancing_matrix</b> (<var>void</var>)<var> const<a name="index-balancing_005fmatrix-638"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const ComplexAEPBALANCE &amp;a</var>)<var><a name="index-operator-_003c_003c-639"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>DET</b> (<var>void</var>)<var><a name="index-DET-640"></a></var><br>
&mdash; :  <b>DET</b> (<var>const DET &amp;a</var>)<var><a name="index-DET-641"></a></var><br>
        </div>

<div class="defun">
&mdash; : DET&amp; <b>operator =</b> (<var>const DET &amp;a</var>)<var><a name="index-operator-_003d-642"></a></var><br>
        </div>

<div class="defun">
&mdash; : int <b>value_will_overflow</b> (<var>void</var>)<var> const<a name="index-value_005fwill_005foverflow-643"></a></var><br>
&mdash; : int <b>value_will_underflow</b> (<var>void</var>)<var> const<a name="index-value_005fwill_005funderflow-644"></a></var><br>
        </div>

<div class="defun">
&mdash; : double <b>coefficient</b> (<var>void</var>)<var> const<a name="index-coefficient-645"></a></var><br>
&mdash; : int <b>exponent</b> (<var>void</var>)<var> const<a name="index-exponent-646"></a></var><br>
&mdash; : double <b>value</b> (<var>void</var>)<var> const<a name="index-value-647"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const DET &amp;a</var>)<var><a name="index-operator-_003c_003c-648"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>ComplexDET</b> (<var>void</var>)<var><a name="index-ComplexDET-649"></a></var><br>
&mdash; :  <b>ComplexDET</b> (<var>const ComplexDET &amp;a</var>)<var><a name="index-ComplexDET-650"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexDET&amp; <b>operator =</b> (<var>const ComplexDET &amp;a</var>)<var><a name="index-operator-_003d-651"></a></var><br>
        </div>

<div class="defun">
&mdash; : int <b>value_will_overflow</b> (<var>void</var>)<var> const<a name="index-value_005fwill_005foverflow-652"></a></var><br>
&mdash; : int <b>value_will_underflow</b> (<var>void</var>)<var> const<a name="index-value_005fwill_005funderflow-653"></a></var><br>
        </div>

<div class="defun">
&mdash; : Complex <b>coefficient</b> (<var>void</var>)<var> const<a name="index-coefficient-654"></a></var><br>
&mdash; : int <b>exponent</b> (<var>void</var>)<var> const<a name="index-exponent-655"></a></var><br>
&mdash; : Complex <b>value</b> (<var>void</var>)<var> const<a name="index-value-656"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const ComplexDET &amp;a</var>)<var><a name="index-operator-_003c_003c-657"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>GEPBALANCE</b> (<var>void</var>)<var><a name="index-GEPBALANCE-658"></a></var><br>
&mdash; :  <b>GEPBALANCE</b> (<var>const Matrix &amp;a, const Matrix &amp;, const char *balance_job</var>)<var><a name="index-GEPBALANCE-659"></a></var><br>
&mdash; :  <b>GEPBALANCE</b> (<var>const GEPBALANCE &amp;a</var>)<var><a name="index-GEPBALANCE-660"></a></var><br>
        </div>

<div class="defun">
&mdash; : GEPBALANCE&amp; <b>operator =</b> (<var>const GEPBALANCE &amp;a</var>)<var><a name="index-operator-_003d-661"></a></var><br>
        </div>

<div class="defun">
&mdash; : Matrix <b>balanced_a_matrix</b> (<var>void</var>)<var> const<a name="index-balanced_005fa_005fmatrix-662"></a></var><br>
&mdash; : Matrix <b>balanced_b_matrix</b> (<var>void</var>)<var> const<a name="index-balanced_005fb_005fmatrix-663"></a></var><br>
&mdash; : Matrix <b>left_balancing_matrix</b> (<var>void</var>)<var> const<a name="index-left_005fbalancing_005fmatrix-664"></a></var><br>
&mdash; : Matrix <b>right_balancing_matrix</b> (<var>void</var>)<var> const<a name="index-right_005fbalancing_005fmatrix-665"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const GEPBALANCE &amp;a</var>)<var><a name="index-operator-_003c_003c-666"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>CHOL</b> (<var>void</var>)<var><a name="index-CHOL-667"></a></var><br>
&mdash; :  <b>CHOL</b> (<var>const Matrix &amp;a</var>)<var><a name="index-CHOL-668"></a></var><br>
&mdash; :  <b>CHOL</b> (<var>const Matrix &amp;a, int &amp;info</var>)<var><a name="index-CHOL-669"></a></var><br>
&mdash; :  <b>CHOL</b> (<var>const CHOL &amp;a</var>)<var><a name="index-CHOL-670"></a></var><br>
        </div>

<div class="defun">
&mdash; : CHOL&amp; <b>operator =</b> (<var>const CHOL &amp;a</var>)<var><a name="index-operator-_003d-671"></a></var><br>
        </div>

<div class="defun">
&mdash; : Matrix <b>chol_matrix</b> (<var>void</var>)<var> const<a name="index-chol_005fmatrix-672"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const CHOL &amp;a</var>)<var><a name="index-operator-_003c_003c-673"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>ComplexCHOL</b> (<var>void</var>)<var><a name="index-ComplexCHOL-674"></a></var><br>
&mdash; :  <b>ComplexCHOL</b> (<var>const ComplexMatrix &amp;a</var>)<var><a name="index-ComplexCHOL-675"></a></var><br>
&mdash; :  <b>ComplexCHOL</b> (<var>const ComplexMatrix &amp;a, int &amp;info</var>)<var><a name="index-ComplexCHOL-676"></a></var><br>
&mdash; :  <b>ComplexCHOL</b> (<var>const ComplexCHOL &amp;a</var>)<var><a name="index-ComplexCHOL-677"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexCHOL&amp; <b>operator =</b> (<var>const ComplexCHOL &amp;a</var>)<var><a name="index-operator-_003d-678"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexMatrix <b>chol_matrix</b> (<var>void</var>)<var> const<a name="index-chol_005fmatrix-679"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const ComplexCHOL &amp;a</var>)<var><a name="index-operator-_003c_003c-680"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>HESS</b> (<var>void</var>)<var><a name="index-HESS-681"></a></var><br>
&mdash; :  <b>HESS</b> (<var>const Matrix &amp;a</var>)<var><a name="index-HESS-682"></a></var><br>
&mdash; :  <b>HESS</b> (<var>const Matrix&amp;a, int &amp;info</var>)<var><a name="index-HESS-683"></a></var><br>
&mdash; :  <b>HESS</b> (<var>const HESS &amp;a</var>)<var><a name="index-HESS-684"></a></var><br>
        </div>

<div class="defun">
&mdash; : HESS&amp; <b>operator =</b> (<var>const HESS &amp;a</var>)<var><a name="index-operator-_003d-685"></a></var><br>
        </div>

<div class="defun">
&mdash; : Matrix <b>hess_matrix</b> (<var>void</var>)<var> const<a name="index-hess_005fmatrix-686"></a></var><br>
&mdash; : Matrix <b>unitary_hess_matrix</b> (<var>void</var>)<var> const<a name="index-unitary_005fhess_005fmatrix-687"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const HESS &amp;a</var>)<var><a name="index-operator-_003c_003c-688"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>ComplexHESS</b> (<var>void</var>)<var><a name="index-ComplexHESS-689"></a></var><br>
&mdash; :  <b>ComplexHESS</b> (<var>const ComplexMatrix &amp;a</var>)<var><a name="index-ComplexHESS-690"></a></var><br>
&mdash; :  <b>ComplexHESS</b> (<var>const ComplexMatrix &amp;a, int &amp;info</var>)<var><a name="index-ComplexHESS-691"></a></var><br>
&mdash; :  <b>ComplexHESS</b> (<var>const ComplexHESS &amp;a</var>)<var><a name="index-ComplexHESS-692"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexHESS&amp; <b>operator =</b> (<var>const ComplexHESS &amp;a</var>)<var><a name="index-operator-_003d-693"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexMatrix <b>hess_matrix</b> (<var>void</var>)<var> const<a name="index-hess_005fmatrix-694"></a></var><br>
&mdash; : ComplexMatrix <b>unitary_hess_matrix</b> (<var>void</var>)<var> const<a name="index-unitary_005fhess_005fmatrix-695"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const ComplexHESS &amp;a</var>)<var><a name="index-operator-_003c_003c-696"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>SCHUR</b> (<var>void</var>)<var><a name="index-SCHUR-697"></a></var><br>
&mdash; :  <b>SCHUR</b> (<var>const Matrix &amp;a, const char *ord</var>)<var><a name="index-SCHUR-698"></a></var><br>
&mdash; :  <b>SCHUR</b> (<var>const Matrix &amp;a, const char *ord, int &amp;info</var>)<var><a name="index-SCHUR-699"></a></var><br>
&mdash; :  <b>SCHUR</b> (<var>const SCHUR &amp;a, const char *ord</var>)<var><a name="index-SCHUR-700"></a></var><br>
        </div>

<div class="defun">
&mdash; : SCHUR&amp; <b>operator =</b> (<var>const SCHUR &amp;a</var>)<var><a name="index-operator-_003d-701"></a></var><br>
        </div>

<div class="defun">
&mdash; : Matrix <b>schur_matrix</b> (<var>void</var>)<var> const<a name="index-schur_005fmatrix-702"></a></var><br>
&mdash; : Matrix <b>unitary_matrix</b> (<var>void</var>)<var> const<a name="index-unitary_005fmatrix-703"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const SCHUR &amp;a</var>)<var><a name="index-operator-_003c_003c-704"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>ComplexSCHUR</b> (<var>void</var>)<var><a name="index-ComplexSCHUR-705"></a></var><br>
&mdash; :  <b>ComplexSCHUR</b> (<var>const ComplexMatrix &amp;a, const char *ord</var>)<var><a name="index-ComplexSCHUR-706"></a></var><br>
&mdash; :  <b>ComplexSCHUR</b> (<var>const ComplexMatrix &amp;a, const char *ord, int &amp;info</var>)<var><a name="index-ComplexSCHUR-707"></a></var><br>
&mdash; :  <b>ComplexSCHUR</b> (<var>const ComplexSCHUR &amp;a, const char *ord</var>)<var><a name="index-ComplexSCHUR-708"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexSCHUR&amp; <b>operator =</b> (<var>const ComplexSCHUR &amp;a</var>)<var><a name="index-operator-_003d-709"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexMatrix <b>schur_matrix</b> (<var>void</var>)<var> const<a name="index-schur_005fmatrix-710"></a></var><br>
&mdash; : ComplexMatrix <b>unitary_matrix</b> (<var>void</var>)<var> const<a name="index-unitary_005fmatrix-711"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const ComplexSCHUR &amp;a</var>)<var><a name="index-operator-_003c_003c-712"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>SVD</b> (<var>void</var>)<var><a name="index-SVD-713"></a></var><br>
&mdash; :  <b>SVD</b> (<var>const Matrix &amp;a</var>)<var><a name="index-SVD-714"></a></var><br>
&mdash; :  <b>SVD</b> (<var>const Matrix &amp;a, int &amp;info</var>)<var><a name="index-SVD-715"></a></var><br>
&mdash; :  <b>SVD</b> (<var>const SVD &amp;a</var>)<var><a name="index-SVD-716"></a></var><br>
        </div>

<div class="defun">
&mdash; : SVD&amp; <b>operator =</b> (<var>const SVD &amp;a</var>)<var><a name="index-operator-_003d-717"></a></var><br>
        </div>

<div class="defun">
&mdash; : DiagMatrix <b>singular_values</b> (<var>void</var>)<var> const<a name="index-singular_005fvalues-718"></a></var><br>
&mdash; : Matrix <b>left_singular_matrix</b> (<var>void</var>)<var> const<a name="index-left_005fsingular_005fmatrix-719"></a></var><br>
&mdash; : Matrix <b>right_singular_matrix</b> (<var>void</var>)<var> const<a name="index-right_005fsingular_005fmatrix-720"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const SVD &amp;a</var>)<var><a name="index-operator-_003c_003c-721"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>ComplexSVD</b> (<var>void</var>)<var><a name="index-ComplexSVD-722"></a></var><br>
&mdash; :  <b>ComplexSVD</b> (<var>const ComplexMatrix &amp;a</var>)<var><a name="index-ComplexSVD-723"></a></var><br>
&mdash; :  <b>ComplexSVD</b> (<var>const ComplexMatrix &amp;a, int &amp;info</var>)<var><a name="index-ComplexSVD-724"></a></var><br>
&mdash; :  <b>ComplexSVD</b> (<var>const ComplexSVD &amp;a</var>)<var><a name="index-ComplexSVD-725"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexSVD&amp; <b>operator =</b> (<var>const ComplexSVD &amp;a</var>)<var><a name="index-operator-_003d-726"></a></var><br>
        </div>

<div class="defun">
&mdash; : DiagMatrix <b>singular_values</b> (<var>void</var>)<var> const<a name="index-singular_005fvalues-727"></a></var><br>
&mdash; : ComplexMatrix <b>left_singular_matrix</b> (<var>void</var>)<var> const<a name="index-left_005fsingular_005fmatrix-728"></a></var><br>
&mdash; : ComplexMatrix <b>right_singular_matrix</b> (<var>void</var>)<var> const<a name="index-right_005fsingular_005fmatrix-729"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const ComplexSVD &amp;a</var>)<var><a name="index-operator-_003c_003c-730"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>EIG</b> (<var>void</var>)<var><a name="index-EIG-731"></a></var><br>
&mdash; :  <b>EIG</b> (<var>const Matrix &amp;a</var>)<var><a name="index-EIG-732"></a></var><br>
&mdash; :  <b>EIG</b> (<var>const Matrix &amp;a, int &amp;info</var>)<var><a name="index-EIG-733"></a></var><br>
&mdash; :  <b>EIG</b> (<var>const ComplexMatrix &amp;a</var>)<var><a name="index-EIG-734"></a></var><br>
&mdash; :  <b>EIG</b> (<var>const ComplexMatrix &amp;a, int &amp;info</var>)<var><a name="index-EIG-735"></a></var><br>
&mdash; :  <b>EIG</b> (<var>const EIG &amp;a</var>)<var><a name="index-EIG-736"></a></var><br>
        </div>

<div class="defun">
&mdash; : EIG&amp; <b>operator =</b> (<var>const EIG &amp;a</var>)<var><a name="index-operator-_003d-737"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexColumnVector <b>eigenvalues</b> (<var>void</var>)<var> const<a name="index-eigenvalues-738"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexMatrix <b>eigenvectors</b> (<var>void</var>)<var> const<a name="index-eigenvectors-739"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const EIG &amp;a</var>)<var><a name="index-operator-_003c_003c-740"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>LU</b> (<var>void</var>)<var><a name="index-LU-741"></a></var><br>
&mdash; :  <b>LU</b> (<var>const Matrix &amp;a</var>)<var><a name="index-LU-742"></a></var><br>
&mdash; :  <b>LU</b> (<var>const LU &amp;a</var>)<var><a name="index-LU-743"></a></var><br>
        </div>

<div class="defun">
&mdash; : LU&amp; <b>operator =</b> (<var>const LU &amp;a</var>)<var><a name="index-operator-_003d-744"></a></var><br>
        </div>

<div class="defun">
&mdash; : Matrix <b>L</b> (<var>void</var>)<var> const<a name="index-L-745"></a></var><br>
&mdash; : Matrix <b>U</b> (<var>void</var>)<var> const<a name="index-U-746"></a></var><br>
&mdash; : Matrix <b>P</b> (<var>void</var>)<var> const<a name="index-P-747"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const LU &amp;a</var>)<var><a name="index-operator-_003c_003c-748"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>ComplexLU</b> (<var>void</var>)<var><a name="index-ComplexLU-749"></a></var><br>
&mdash; :  <b>ComplexLU</b> (<var>const ComplexMatrix &amp;a</var>)<var><a name="index-ComplexLU-750"></a></var><br>
&mdash; :  <b>ComplexLU</b> (<var>const ComplexLU &amp;a</var>)<var><a name="index-ComplexLU-751"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexLU&amp; <b>operator =</b> (<var>const ComplexLU &amp;a</var>)<var><a name="index-operator-_003d-752"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexMatrix <b>L</b> (<var>void</var>)<var> const<a name="index-L-753"></a></var><br>
&mdash; : ComplexMatrix <b>U</b> (<var>void</var>)<var> const<a name="index-U-754"></a></var><br>
&mdash; : Matrix <b>P</b> (<var>void</var>)<var> const<a name="index-P-755"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const ComplexLU &amp;a</var>)<var><a name="index-operator-_003c_003c-756"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>QR</b> (<var>void</var>)<var><a name="index-QR-757"></a></var><br>
&mdash; :  <b>QR</b> (<var>const Matrix &amp;A</var>)<var><a name="index-QR-758"></a></var><br>
&mdash; :  <b>QR</b> (<var>const QR &amp;a</var>)<var><a name="index-QR-759"></a></var><br>
        </div>

<div class="defun">
&mdash; : QR&amp; <b>operator =</b> (<var>const QR &amp;a</var>)<var><a name="index-operator-_003d-760"></a></var><br>
        </div>

<div class="defun">
&mdash; : Matrix <b>Q</b> (<var>void</var>)<var> const<a name="index-Q-761"></a></var><br>
&mdash; : Matrix <b>R</b> (<var>void</var>)<var> const<a name="index-R-762"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const QR &amp;a</var>)<var><a name="index-operator-_003c_003c-763"></a></var><br>
        </div>

<div class="defun">
&mdash; :  <b>ComplexQR</b> (<var>void</var>)<var><a name="index-ComplexQR-764"></a></var><br>
&mdash; :  <b>ComplexQR</b> (<var>const ComplexMatrix &amp;A</var>)<var><a name="index-ComplexQR-765"></a></var><br>
&mdash; :  <b>ComplexQR</b> (<var>const ComplexQR &amp;a</var>)<var><a name="index-ComplexQR-766"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexQR&amp; <b>operator =</b> (<var>const ComplexQR &amp;a</var>)<var><a name="index-operator-_003d-767"></a></var><br>
        </div>

<div class="defun">
&mdash; : ComplexMatrix <b>Q</b> (<var>void</var>)<var> const<a name="index-Q-768"></a></var><br>
&mdash; : ComplexMatrix <b>R</b> (<var>void</var>)<var> const<a name="index-R-769"></a></var><br>
        </div>

<div class="defun">
&mdash; : ostream&amp; <b>operator &lt;&lt;</b> (<var>ostream &amp;os, const ComplexQR &amp;a</var>)<var><a name="index-operator-_003c_003c-770"></a></var><br>
        </div>

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