Name
eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix — Compute the eigenvalues and optionally eigenvectors of a symmetric
matrix.
The operator eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix computes all
eigenvalues and, optionally, eigenvectors of the symmetric
MatrixMatrixMatrixMatrixMatrixmatrix. The matrix is defined by the matrix handle
MatrixIDMatrixIDMatrixIDMatrixIDMatrixIDmatrixID. 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 EigenvaluesIDEigenvaluesIDEigenvaluesIDEigenvaluesIDEigenvaluesIDeigenvaluesID and
EigenvectorsIDEigenvectorsIDEigenvectorsIDEigenvectorsIDEigenvectorsIDeigenvectorsID of the matrices EigenvaluesEigenvaluesEigenvaluesEigenvaluesEigenvalueseigenvalues and
EigenvectorsEigenvectorsEigenvectorsEigenvectorsEigenvectorseigenvectors. Access to the elements of the matrices is
possible e.g. with the operator get_full_matrixget_full_matrixGetFullMatrixget_full_matrixGetFullMatrixGetFullMatrix.
The computation of eigenvectors can be selected via
ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectors = 'true'"true""true""true""true""true" or
ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectors = 'false'"false""false""false""false""false".
Example:
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.
- Multithreading type: reentrant (runs in parallel with non-exclusive operators).
- Multithreading scope: global (may be called from any thread).
- Processed without parallelization.
Matrix handle of the input matrix.
Computation of the eigenvectors.
Default value:
'false'
"false"
"false"
"false"
"false"
"false"
List of values: 'false'"false""false""false""false""false", 'true'"true""true""true""true""true"
Matrix handle with the eigenvalues.
Matrix handle with the eigenvectors.
If the parameters are valid, the operator
eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix returns the value 2 (H_MSG_TRUE). If
necessary, an exception is raised.
create_matrixcreate_matrixCreateMatrixcreate_matrixCreateMatrixCreateMatrix
get_full_matrixget_full_matrixGetFullMatrixget_full_matrixGetFullMatrixGetFullMatrix,
get_value_matrixget_value_matrixGetValueMatrixget_value_matrixGetValueMatrixGetValueMatrix
eigenvalues_general_matrixeigenvalues_general_matrixEigenvaluesGeneralMatrixeigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrix
generalized_eigenvalues_symmetric_matrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrix,
generalized_eigenvalues_general_matrixgeneralized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixgeneralized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrix
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.
Foundation