eigenvalues_general_matrixT_eigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixeigenvalues_general_matrix (Operator)

Name

eigenvalues_general_matrixT_eigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixeigenvalues_general_matrix — Compute the eigenvalues and optionally the eigenvectors of a general matrix.

Signature

Description

The operator eigenvalues_general_matrixeigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixeigenvalues_general_matrix computes all eigenvalues and, optionally, the left or right eigenvectors of a square, general MatrixMatrixMatrixMatrixmatrixmatrix. The matrix is defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixIDmatrix_id. The computed eigenvectors have the norm 1.

The operator generates the new matrices EigenvaluesRealEigenvaluesRealEigenvaluesRealEigenvaluesRealeigenvaluesRealeigenvalues_real and EigenvaluesImagEigenvaluesImagEigenvaluesImagEigenvaluesImageigenvaluesImageigenvalues_imag with the real and the imaginary parts of the computed eigenvalues. Each matrix has one column and n rows, where n is the number of rows of the input MatrixMatrixMatrixMatrixmatrixmatrix. In contrast to the operator eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrix, the order of the eigenvalues is not defined. The operator returns the matrix handles EigenvaluesRealIDEigenvaluesRealIDEigenvaluesRealIDEigenvaluesRealIDeigenvaluesRealIDeigenvalues_real_id and EigenvaluesImagIDEigenvaluesImagIDEigenvaluesImagIDEigenvaluesImagIDeigenvaluesImagIDeigenvalues_imag_id. If desired, the real and imaginary parts of the computed eigenvectors are stored in the new matrices EigenvectorsRealEigenvectorsRealEigenvectorsRealEigenvectorsRealeigenvectorsRealeigenvectors_real and EigenvectorsImagEigenvectorsImagEigenvectorsImagEigenvectorsImageigenvectorsImageigenvectors_imag. For this, the operator returns valid matrix handles EigenvectorsRealIDEigenvectorsRealIDEigenvectorsRealIDEigenvectorsRealIDeigenvectorsRealIDeigenvectors_real_id and EigenvectorsImagIDEigenvectorsImagIDEigenvectorsImagIDEigenvectorsImagIDeigenvectorsImagIDeigenvectors_imag_id. Access to the elements of the matrix is possible e.g. with the operator get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrixget_full_matrix.

The computation type of eigenvectors can be selected via the parameter ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectorscompute_eigenvectors. If ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectorscompute_eigenvectors = 'none'"none""none""none""none""none", no eigenvectors are computed. If 'left'"left""left""left""left""left" is selected, the left eigenvalues are computed. If 'right'"right""right""right""right""right" is selected, the right eigenvalues are computed.

Example:

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_general_matrixeigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixeigenvalues_general_matrix returns the value 2 (H_MSG_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, get_diagonal_matrixget_diagonal_matrixGetDiagonalMatrixGetDiagonalMatrixGetDiagonalMatrixget_diagonal_matrix

See also

eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrix, 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