Performs the Schur decomposition of a square matrix. Wire data to the Input Matrix input to determine the polymorphic instance to use or manually select the instance.


icon

Inputs/Outputs

  • c2dcdb.png Input Matrix —

    Input Matrix must be a square complex matrix.

  • cbool.png compute Schur vectors? —

    compute Schur vectors? specifies whether the VI calculates Schur Vectors. The default is FALSE.

  • cu16.png order —

    order specifies how to order the Eigenvalues and the corresponding Schur Form and Schur Vectors.

    0No Reorder (default)—Does not change the order of the Eigenvalues.
    1Real Ascending—Lists the Eigenvalues in ascending order according to their real parts.
    2Real Descending—Lists the Eigenvalues in descending order according to their real parts.
    3Magnitude Ascending—Lists the Eigenvalues in ascending order according to their magnitudes.
    4Magnitude Descending—Lists the Eigenvalues in descending order according to their magnitudes.
  • i2dcdb.png Schur Form —

    Schur Form returns the upper triangular matrix.

  • i2dcdb.png Schur Vectors —

    Schur Vectors returns the unitary matrix.

  • i1dcdb.png Eigenvalues —

    Eigenvalues returns a complex vector that contains all the computed eigenvalues of Input Matrix.

  • 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.

    • The following expression defines the Schur decomposition of a square n × n matrix A.

    A = QSQH

    where S is in Schur form, and QH is the conjugate transpose of matrix Q.

    Real Matrix

    For a real matrix A, Q is an n × n orthogonal matrix. S is a block upper triangular matrix in real Schur form, whose elements on the main diagonal are all 1 × 1 or 2 × 2 blocks, as shown in the following matrix.

    where Sii are square blocks of dimension 1 or 2, and i = 1, 2, …, m.

    Complex Matrix

    For a complex matrix A, Q is an n × n unitary matrix. S is an upper triangular matrix in complex Schur form.