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.TH gspec G "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
gspec - eigenvalues of matrix pencil
.SH CALLING SEQUENCE
.nf
[al,be]=gspec(A,E)
[al,be,Z]=gspec(A,E)
.fi
.SH PARAMETERS
.TP 10
A, E
: real square matrices
.TP
al, be
: real vectors
.TP
Z
: real square non-singular matrix
.SH DESCRIPTION
.Vb [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 \fVal./be\fR and if \fVbe(i) = 0\fR the ith
eigenvalue is at infinity. (For \fVE = eye(A), al./be\fR is \fVspec(A)\fR).
.LP
.Vb [al,be,Z] = gspec(A,E)
returns in addition the matrix \fVZ\fR of generalized
right eigenvectors of the pencil.
.SH EXAMPLE
.nf
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
.fi
.SH SEE ALSO
gschur, balanc, spec, kroneck
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