Finds the eigenvalues and right eigenvectors of the square Input Matrix. Wire data to the Input Matrix input to determine the polymorphic instance to use or manually select the instance.


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Inputs/Outputs

  • c2dcdb.png Input Matrix —

    Input Matrix must be an n-by-n square, complex matrix, where n is the number of rows and columns of Input Matrix.

  • ci32.png matrix type —

    matrix type is the type of Input Matrix. A symmetric matrix needs less computation than an unsymmetrical matrix. A Hermitian matrix always has real eigenvalues.

    0General (default)
    1Hermitian
  • ci32.png output option —

    output option determines whether the VI computes Eigenvectors.

    0eigenvalues
    1eigenvalues and vectors (default)
  • i1dcdb.png Eigenvalues —

    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 Hermitian.

  • i2dcdb.png Eigenvectors —

    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 Euclidean norm equals 1.

    If output option is set to eigenvalues, the VI returns Eigenvectors as an empty array.

  • ii32.png error —

    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.

    • Real

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

    AX = λX

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

    Complex

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

    AX = λX

    where A represents an n-by-n Input Matrix, X represents a vector with n elements, and λ is a scalar. The n values of λ 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. This VI returns the real eigenvalues in ascending order if the Input Matrix is a Hermitian matrix.

    Examples

    Refer to the following example files included with LabVIEW.

    • labview\examples\Mathematics\Linear Algebra\Linear Algebra Calculator.vi
    • labview\examples\Mathematics\Differential Equations - ODE\Linear Differential Equation Solving.vi