Polynomial Eigenvalues and Vectors (Not in Base Package)

Solves the polynomial eigenvalue problem. You can use this polymorphic VI to solve the polynomial eigenvalue problem for real polynomials or complex polynomials. The data type you wire to the Input Matrices input determines the polymorphic instance to use. Details  

Polynomial Eigenvalues and Vectors (DBL)

	Input Matrices is a 3D array of size n*n*p and contains square input matrixes of the same size. The input matrixes must be square. The matrixes are in ascending order of power for Eigenvalues.
	output option determines whether the VI computes Eigenvectors. 0 eigenvalues 1 eigenvalues & vectors (default)
	Eigenvalues is a complex vector of n*p elements and contains all of the computed eigenvalues.
	Eigenvectors is an n × (n*p) complex matrix and contains all of the computed eigenvectors in its columns.
	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.

Polynomial Eigenvalues and Vectors (CDB)

	Input Matrices is a 3D array of size n*n*p and contains square input matrixes of the same size. The input matrixes must be square. The matrixes are in ascending order of power for Eigenvalues.
	output option determines whether the VI computes Eigenvectors. 0 eigenvalues 1 eigenvalues & vectors (default)
	Eigenvalues is a complex vector of n*p elements and contains all of the computed eigenvalues.
	Eigenvectors is an n × (n*p) complex matrix and contains all of the computed eigenvectors in its columns.
	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.

Polynomial Eigenvalues and Vectors Details

The following equation defines the polynomial eigenvalue problem.

where

C₀, C₁, …, C_{p – 1} are square n × n matrixes in Input Matrices

_j is the jth element in Eigenvalues

x_j has length n and is the jth column in Eigenvectors with j = 0, 1, …, n*p – 1

If p = 1, the VI calculates eigenvalues and eigenvectors using the following equation.

C₀x_j = _jx_j

If p = 2, the VI calculates generalized eigenvalues and eigenvectors using the following equation.

C₀x_j = –_jC₁x_j