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308 3. Reference Manual
r v ⩵
v H A ΛB
r u ⩵ A ΛBu
Compute the residual
norms.
In[6]:= {L2Norm[Conjugate[v].(A − lambda*B)],
L2Norm[(A − lambda*B).u]}
Out[6]= 5.66105 10 16 , 3.29562 10 16
3.8.2 GeneralizedEigenvalues
GeneralizedEigenvalues[A, B]
Command structure of GeneralizedEigenvalues.
computes the eigenvalues of the matrix pencil A B where
A and B must be real-valued square matrices
GeneralizedEigenvalues computes the eigenvalues of a matrix pencil A B by the QZ algorithm.
The function returns a list of the finite Λ i that satisfy the GEP defined by A B.
Note that this function is accessible only if the global Analog Insydes option UseExternals is set to
True and if a native version of the external MathLink module QZ.exe is available for your machine
(see Section 3.13.4).
See also: GeneralizedEigensystem (Section 3.8.1), UseExternals (Section 3.14.7).
Examples
Load Analog Insydes.
Define two square
real-valued matrices.
Compute the eigenvalues
of A B.
In[1]:=