gschur(G)

NAME
gschur - generalized Schur form (matrix pencils).

CALLING SEQUENCE
[As,Es]=gschur(A,E)
[As,Es,Q,Z]=gschur(A,E)
[As,Es,Q,dim] = gschur(A,E,flag)
[As,Es,Q,dim]= gschur(A,E,extern)

PARAMETERS

A, E
    : two real square matrices

flag
    : character string ('c' or 'd')

extern
    : Scilab ``external'' function (usual case). Could be also a list or a character string

As,Es
    : two real square matrices

Q, Z
    : two non-singular real matrices

dim : integer (dimension of subspace)

DESCRIPTION

Schur form of matrix pencils (QZ algorithm)
[As,Es] = gschur(A,E)
produces a quasi triangular As matrix and a triangular Es matrix which are the generalized Schur form of the pair A, E.

[As,Es,Q,Z] = gschur(A,E)
returns in addition two unitary matrices Q and Z such that As=Q*A*Z and Es=Q*E*Z.

Ordered stable form
[As,Es,Q,dim] = gschur(A,E,'c')
returns the real generalized Schur form of the pencil s*E-A. In addition, the dim first columns of Q span a basis of the right eigenspace associated with eigenvalues with negative real parts (stable "continuous time" generalized eigenspace).
[As,Es,Q,dim] = gschur(A,E,'d')
returns the real generalized Schur form of the pencil s*E-A. In addition, the dim first columns of Q make a basis of the right eigenspace associated with eigenvalues with magnitude lower than 1 (stable "discrete time" generalized eigenspace).

General subspace
[As,Es,Q,dim] = gschur(A,E,extern)
returns the real generalized Schur form of the pencil s*E-A. In addition, the dim first columns of Q make a basis of the right eigenspace associated with eigenvalues of the pencil which are selected according to a rule which is given by the scilab function extern. (See schur for definition of this function).

SEE ALSO
external, gspec, pencan, penlaur, coffg, balanc