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gspec(G) Scilab Function gspec(G)
NAME
gspec - eigenvalues of matrix pencil
CALLING SEQUENCE
[al,be]=gspec(A,E)
[al,be,Z]=gspec(A,E)
PARAMETERS
A, E : real square matrices
al, be : real vectors
Z : real square non-singular matrix
DESCRIPTION
[al,be] = gspec(A,E) returns the spectrum of the matrix pencil s E - A,
i.e. the roots of the polynomial matrix s E - A. The eigenvalues are given
by al./be and if be(i) = 0 the ith eigenvalue is at infinity. (For E =
eye(A), al./be is spec(A)).
[al,be,Z] = gspec(A,E) returns in addition the matrix Z of generalized
right eigenvectors of the pencil.
EXAMPLE
A=rand(3,3);
[al,be,Z] = gspec(A,eye(A));al./be
clean(inv(Z)*A*Z) //displaying the eigenvalues (generic matrix)
A=A+%i*rand(A);E=rand(A);
roots(det(%s*E-A)) //complex case
SEE ALSO
gschur, balanc, spec, kroneck
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