Return type of eigenvalues()

Real part of Scalar

See also

MatrixBase::adjoint() const

See also

MatrixBase::coeff()

Warning

the coordinates must fit into the referenced triangular part

See also

MatrixBase::coeffRef()

Warning

the coordinates must fit into the referenced triangular part

See also

MatrixBase::conjugate() const

Returns

an expression of the complex conjugate of *this if Cond==true, returns *this otherwise.

Returns

a const expression of the main diagonal of the matrix *this

This method simply returns the diagonal of the nested expression, thus by-passing the SelfAdjointView decorator.

See also

MatrixBase::diagonal(), class Diagonal

Computes the eigenvalues of a matrix.

Returns

Column vector containing the eigenvalues.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues> 

This function computes the eigenvalues with the help of the SelfAdjointEigenSolver class. The eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix.

Example:

MatrixXd ones = MatrixXd::Ones(3,3);
VectorXd eivals = ones.selfadjointView<Lower>().eigenvalues();
cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;

Output:

The eigenvalues of the 3x3 matrix of ones are:
-3.09e-16
        0
        3

See also

SelfAdjointEigenSolver::eigenvalues(), MatrixBase::eigenvalues()

This is defined in the Cholesky module.

#include <Eigen/Cholesky> 

Returns

the Cholesky decomposition with full pivoting without square root of *this

See also

MatrixBase::ldlt()

This is defined in the Cholesky module.

#include <Eigen/Cholesky> 

Returns

the LLT decomposition of *this

See also

SelfAdjointView::llt()

Efficient triangular matrix times vector/matrix product

Computes the L2 operator norm.

Returns

Operator norm of the matrix.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues> 

This function computes the L2 operator norm of a self-adjoint matrix. For a self-adjoint matrix, the operator norm is the largest eigenvalue.

The current implementation uses the eigenvalues of the matrix, as computed by eigenvalues(), to compute the operator norm of the matrix.

Example:

MatrixXd ones = MatrixXd::Ones(3,3);
cout << "The operator norm of the 3x3 matrix of ones is "
     << ones.selfadjointView<Lower>().operatorNorm() << endl;

Output:

The operator norm of the 3x3 matrix of ones is 3

See also

eigenvalues(), MatrixBase::operatorNorm()

Perform a symmetric rank 2 update of the selfadjoint matrix *this: \( this = this + \alpha u v^* + conj(\alpha) v u^* \)

Returns

a reference to *this

The vectors u and v must be column vectors, however they can be a adjoint expression without any overhead. Only the meaningful triangular part of the matrix is updated, the rest is left unchanged.

See also

rankUpdate(const MatrixBase<DerivedU>&, Scalar)

Perform a symmetric rank K update of the selfadjoint matrix *this: \( this = this + \alpha ( u u^* ) \) where u is a vector or matrix.

Returns

a reference to *this

Note that to perform \( this = this + \alpha ( u^* u ) \) you can simply call this function with u.adjoint().

See also

rankUpdate(const MatrixBase<DerivedU>&, const MatrixBase<DerivedV>&, Scalar)

See also

MatrixBase::transpose()

See also

MatrixBase::transpose() const

Returns

an expression of a triangular view extracted from the current selfadjoint view of a given triangular part

The parameter TriMode can have the following values: Upper, StrictlyUpper, UnitUpper, Lower, StrictlyLower, UnitLower.

If TriMode references the same triangular part than *this, then this method simply return a TriangularView of the nested expression, otherwise, the nested expression is first transposed, thus returning a TriangularView<Transpose<MatrixType>> object.

See also

MatrixBase::triangularView(), class TriangularView