eigenvalues_symmetric_matrixT_eigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrix (Operator)

Name

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

Signature

Description

The operator eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrix computes all eigenvalues and, optionally, eigenvectors of the symmetric MatrixMatrixMatrixMatrixmatrixmatrix. The matrix is defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixIDmatrix_id. On output, a new matrix EigenvaluesEigenvaluesEigenvaluesEigenvalueseigenvalueseigenvalues with the eigenvalues in ascending order and, optionally, a new matrix EigenvectorsEigenvectorsEigenvectorsEigenvectorseigenvectorseigenvectors with the eigenvectors is created. The operator returns the matrix handles EigenvaluesIDEigenvaluesIDEigenvaluesIDEigenvaluesIDeigenvaluesIDeigenvalues_id and EigenvectorsIDEigenvectorsIDEigenvectorsIDEigenvectorsIDeigenvectorsIDeigenvectors_id of the matrices EigenvaluesEigenvaluesEigenvaluesEigenvalueseigenvalueseigenvalues and EigenvectorsEigenvectorsEigenvectorsEigenvectorseigenvectorseigenvectors. Access to the elements of the matrices is possible e.g. with the operator get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrixget_full_matrix.

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

Example:

Attention

The upper triangular part of the input MatrixMatrixMatrixMatrixmatrixmatrix 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 MatrixMatrixMatrixMatrixmatrixmatrix 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_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrix returns the value TRUE. If necessary, an exception is raised.

Possible Predecessors

create_matrixcreate_matrixCreateMatrixCreateMatrixCreateMatrixcreate_matrix

Possible Successors

get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrixget_full_matrix, get_value_matrixget_value_matrixGetValueMatrixGetValueMatrixGetValueMatrixget_value_matrix

Alternatives

eigenvalues_general_matrixeigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixeigenvalues_general_matrix

See also

generalized_eigenvalues_symmetric_matrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrixgeneralized_eigenvalues_symmetric_matrix, generalized_eigenvalues_general_matrixgeneralized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrixgeneralized_eigenvalues_general_matrix

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