Dew Math for .NET
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Computes generalized eigenvalues and eigenvectors of a non-symmetric matrix.
A generalized eigenvalue for a pair of matrices (A = Self,B) is a scalar lambda or a ratio alpha/beta = lambda, such that A - lambda*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta = 0, and even for both being zero.
The right eigenvector v(j) corresponding to the eigenvalue lambda(j) of (A,B) satisfies:
The left eigenvector u(j) corresponding to the eigenvalue lambda(j) of (A,B) satisfies:
where u(j)**H is the conjugate-transpose of u(j). The individual eigevalues can be computed as:
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