3.8.2 GeneralizedEigenvalues

Command structure of GeneralizedEigenvalues.

GeneralizedEigenvalues computes the eigenvalues of a matrix pencil by the QZ algorithm. The function returns a list of the finite that satisfy the GEP defined by .

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, UseExternals.

Examples

Load Analog Insydes.

In[1]:= <<AnalogInsydes`

Define two square real-valued matrices.

In[2]:= A = {{1, 2}, {-3, 1}};
B = {{1, 4}, { 2, 1}};

Compute the eigenvalues of .

In[3]:= GeneralizedEigenvalues[A, B]

Out[4]=

GeneralizedEigenvalues also works if some or all of the eigenvalues are complex and in the case where or are singular.

Define two further matrices.

In[4]:= B2 = {{1, -5}, {2, 1}};
B3 = {{1, -1}, {0, 0}};

Compute the eigenvalues of .

In[5]:= GeneralizedEigenvalues[A, B2]

Out[7]=

Compute the eigenvalues of .

In[6]:= GeneralizedEigenvalues[A, B3]

Out[8]=