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U:RDoc::NormalClass[iI" EigenvalueDecomposition:ETI"$Matrix::EigenvalueDecomposition;TI" Object;To:RDoc::Markup::Document: @parts[o;;[ o: RDoc::Markup::Paragraph;[I"3Eigenvalues and eigenvectors of a real matrix.;To: RDoc::Markup::BlankLine o; ;[I"=Computes the eigenvalues and eigenvectors of a matrix A.;T@o; ;[I"<If A is diagonalizable, this provides matrices V and D ;TI"Jsuch that A = V*D*V.inv, where D is the diagonal matrix with entries ;TI"Bequal to the eigenvalues and V is formed by the eigenvectors.;T@o; ;[I"AIf A is symmetric, then V is orthogonal and thus A = V*D*V.t;T: @fileI"+lib/matrix/eigenvalue_decomposition.rb;T:0@omit_headings_from_table_of_contents_below0; 0; 0[ [ [ [[I" class;T[[: public[[I"new;TI"+lib/matrix/eigenvalue_decomposition.rb;T[:protected[ [: private[ [I" instance;T[[; [[I"d;F@)[I"eigenvalue_matrix;F@)[I"eigenvalues;F@)[I"eigenvector_matrix;F@)[I"eigenvector_matrix_inv;F@)[I"eigenvectors;F@)[I" to_a;T@)[I" to_ary;F@)[I"v;F@)[I" v_inv;F@)[;[ [;[ [I"build_eigenvectors;F@)[I" cdiv;F@)[I"diagonalize;F@)[I" hessenberg_to_real_schur;F@)[I"reduce_to_hessenberg;F@)[I"tridiagonalize;F@)[ [U:RDoc::Context::Section[i 0o;;[ ; 0; 0[@ I" Matrix;TcRDoc::NormalClass
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