diff options
| author |  Gael Guennebaud <g.gael@free.fr> | 2010-06-10 09:44:52 +0200 |
|---|---|---|
| committer | Gael Guennebaud <g.gael@free.fr> | 2010-06-10 09:44:52 +0200 |
| commit | f8683c409f7524db471e76b1540344ecdc7b0be6 (patch) | |
| tree | fcff5c01d22fff253da76bd3fe9ee2a5a8ad1225 /Eigen/src/Eigenvalues | |
| parent | 41e5625f96b9d9642c1724ff3859e709d9cfe8cb (diff) | |
generalized eigendecomposition doc
Diffstat (limited to 'Eigen/src/Eigenvalues')
| -rw-r--r-- | Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h | 14 |
1 files changed, 9 insertions, 5 deletions
diff --git a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h index 636aa090c..2878a1494 100644 --- a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h +++ b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h @@ -171,7 +171,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver compute(matrix, computeEigenvectors); } - /** \brief Constructor; computes eigendecomposition of given matrix pencil. + /** \brief Constructor; computes generalized eigendecomposition of given matrix pencil. * * \param[in] matA Selfadjoint matrix in matrix pencil. * \param[in] matB Positive-definite matrix in matrix pencil. @@ -183,8 +183,9 @@ template<typename _MatrixType> class SelfAdjointEigenSolver * to compute the eigenvalues and (if requested) the eigenvectors of the * generalized eigenproblem \f$ Ax = \lambda B x \f$ with \a matA the * selfadjoint matrix \f$ A \f$ and \a matB the positive definite matrix - * \f$ B \f$ . The eigenvectors are computed if \a computeEigenvectors is - * true. + * \f$ B \f$. Each eigenvector \f$ x \f$ satisfies the property + * \f$ x^* B x = 1 \f$. The eigenvectors are computed if + * \a computeEigenvectors is true. * * Example: \include SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp * Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.out @@ -236,7 +237,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver */ SelfAdjointEigenSolver& compute(const MatrixType& matrix, bool computeEigenvectors = true); - /** \brief Computes eigendecomposition of given matrix pencil. + /** \brief Computes generalized eigendecomposition of given matrix pencil. * * \param[in] matA Selfadjoint matrix in matrix pencil. * \param[in] matB Positive-definite matrix in matrix pencil. @@ -248,7 +249,10 @@ template<typename _MatrixType> class SelfAdjointEigenSolver * This function computes eigenvalues and (if requested) the eigenvectors * of the generalized eigenproblem \f$ Ax = \lambda B x \f$ with \a matA * the selfadjoint matrix \f$ A \f$ and \a matB the positive definite - * matrix \f$ B \f$. The eigenvalues() function can be used to retrieve + * matrix \f$ B \f$. In addition, each eigenvector \f$ x \f$ + * satisfies the property \f$ x^* B x = 1 \f$. + * + * The eigenvalues() function can be used to retrieve * the eigenvalues. If \p computeEigenvectors is true, then the * eigenvectors are also computed and can be retrieved by calling * eigenvectors(). |