eigenvalues_symmetric_matrixT_eigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix (Operator)

Name

eigenvalues_symmetric_matrixT_eigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix — Compute the eigenvalues and optionally eigenvectors of a symmetric matrix.

Signature

Description

The operator eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix computes all eigenvalues and, optionally, eigenvectors of the symmetric MatrixMatrixMatrixMatrixmatrix. The matrix is defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixID. On output, a new matrix EigenvaluesEigenvaluesEigenvaluesEigenvalueseigenvalues with the eigenvalues in ascending order and, optionally, a new matrix EigenvectorsEigenvectorsEigenvectorsEigenvectorseigenvectors with the eigenvectors is created. The operator returns the matrix handles EigenvaluesIDEigenvaluesIDEigenvaluesIDEigenvaluesIDeigenvaluesID and EigenvectorsIDEigenvectorsIDEigenvectorsIDEigenvectorsIDeigenvectorsID of the matrices EigenvaluesEigenvaluesEigenvaluesEigenvalueseigenvalues and EigenvectorsEigenvectorsEigenvectorsEigenvectorseigenvectors. Access to the elements of the matrices is possible e.g. with the operator get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrix.

The computation of eigenvectors can be selected via ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectors = 'true'"true""true""true""true" or ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectors = 'false'"false""false""false""false".

Example:

Attention

The upper triangular part of the input MatrixMatrixMatrixMatrixmatrix must contain the relevant information of the matrix. The strictly lower triangular part of the matrix is not referenced. If the referenced part of the input MatrixMatrixMatrixMatrixmatrix is not of the specified type, an exception is raised.

Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Processed without parallelization.

Parameters

Result

If the parameters are valid, the operator eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix returns the value 2 (H_MSG_TRUE). If necessary, an exception is raised.

Possible Predecessors

create_matrixcreate_matrixCreateMatrixCreateMatrixCreateMatrix

Possible Successors

get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrix, get_value_matrixget_value_matrixGetValueMatrixGetValueMatrixGetValueMatrix

Alternatives

eigenvalues_general_matrixeigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrix

See also

generalized_eigenvalues_symmetric_matrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrix, generalized_eigenvalues_general_matrixgeneralized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrix

References

David Poole: “Linear Algebra: A Modern Introduction”; Thomson; Belmont; 2006.
Gene H. Golub, Charles F. van Loan: “Matrix Computations”; The Johns Hopkins University Press; Baltimore and London; 1996.

Module

Foundation