EigenValues and Vectors (Not in Base Package)

Finds the eigenvalues and right eigenvectors of the square Input Matrix. You can use this polymorphic VI to find the eigenvalues and right eigenvectors for a real square matrix or a complex square matrix. The data type you wire to the Input Matrix input determines the polymorphic instance to use. Details  Examples

Real EigenValues and Vectors

	Input Matrix is an n-by-n square, real matrix, where n is the number of rows and columns of Input Matrix.
	matrix type is the type of Input Matrix. A symmetric matrix needs less computation than an unsymmetrical matrix. A symmetric matrix always has real eigenvectors and eigenvalues. 0 General (default) 1 Symmetric
	output option determines whether the VI computes Eigenvectors. 0 eigenvalues 1 eigenvalues & vectors (default)
	Eigenvalues is a complex vector of n elements, which contains all of the computed Eigenvalues of the Input Matrix. The Input Matrix could have complex Eigenvalues if it is not symmetric.
	Eigenvectors is an n-by-n complex matrix containing all of the computed Eigenvectors of the Input Matrix. The ith column of Eigenvectors is the eigenvector corresponding to the ith component of the vector, Eigenvalues. Each eigenvector is normalized so that its largest component is always unified. The Input Matrix could have complex Eigenvectors if it is not symmetric. If output option is set to eigenvalues, the VI returns Eigenvectors as an empty array.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Complex EigenValues and Vectors

	Input Matrix must be an n-by-n square, complex matrix, where n is the number of rows and columns of Input Matrix.
	matrix type is the type of Input Matrix. A symmetric matrix needs less computation than an unsymmetrical matrix. A Hermitian matrix always has real eigenvectors and eigenvalues. 0 General (default) 1 Hermitian
	output option determines whether the VI computes Eigenvectors. 0 eigenvalues 1 eigenvalues & vectors (default)
	Eigenvalues is a complex vector of n elements, which contains all of the computed Eigenvalues of the Input Matrix. The Input Matrix could have complex Eigenvalues if it is not symmetric.
	Eigenvectors is an n-by-n complex matrix containing all of the computed Eigenvectors of the Input Matrix. The ith column of Eigenvectors is the eigenvector corresponding to the ith component of the vector, Eigenvalues. Each eigenvector is normalized so that its largest component is always unified. The Input Matrix could have complex Eigenvectors if it is not symmetric. If output option is set to eigenvalues, the VI returns Eigenvectors as an empty array.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

EigenValues and Vectors Details

Real

The eigenvalue problem is to determine the nontrivial solutions to the equation:

AX = X

where A is an n-by-n Input Matrix, X is a vector with n elements, and is a scalar. The n values of that satisfy the equation are the Eigenvalues of A and the corresponding values of X are the right Eigenvectors of A. A symmetric, real matrix always has real eigenvalues and eigenvectors.

Complex

The eigenvalue problem is to determine the nontrivial solutions for the equation:

AX = X

where A represents an n-by-n Input Matrix, X represents a vector with n elements, and is a scalar. The n values of that satisfy the equation are the Eigenvalues of A and the corresponding values of X are the right Eigenvectors of A. A Hermitian matrix always has real eigenvalues.

Examples

Refer to the following VIs for examples of using the EigenValues and Vectors VI:

• Linear Algebra Calculator VI: labview\examples\analysis\linaxmpl.llb

   

• Linear Differential Equation Solving VI: labview\examples\analysis\odexmpl.llb