fstair

computes pencil column echelon form by qz transformations

Calling Sequence

[AE,EE,QE,ZE,blcks,muk,nuk,muk0,nuk0,mnei]=fstair(A,E,Q,Z,stair,rk,tol)

Arguments

:A m x n matrix with real entries. : :tol real positive scalar. : :E column echelon form matrix : :Q m x m unitary matrix : :Z n x n unitary matrix : :stair vector of indexes (see ereduc) : :rk integer, estimated rank of the matrix : :AE m x n matrix with real entries. : :EE column echelon form matrix : :QE m x m unitary matrix : :ZE n x n unitary matrix : :nblcks is the number of submatrices having full row rank >= 0

detected in matrix A.

: :muk: integer array of dimension (n). Contains the column dimensions

mu(k) (k=1,...,nblcks) of the submatrices having full column rank in the pencil sE(eps)-A(eps)

: :nuk: integer array of dimension (m+1). Contains the row dimensions

nu(k) (k=1,...,nblcks) of the submatrices having full row rank in the pencil sE(eps)-A(eps)

: :muk0: integer array of dimension (n). Contains the column

dimensions mu(k) (k=1,...,nblcks) of the submatrices having full column rank in the pencil sE(eps,inf)-A(eps,inf)

: :nuk: integer array of dimension (m+1). Contains the row dimensions

nu(k) (k=1,...,nblcks) of the submatrices having full row rank in the pencil sE(eps,inf)-A(eps,inf)

: :mnei: integer array of dimension (4). mnei(1) = row dimension of

sE(eps)-A(eps)

:

Description

Given a pencil sE-A where matrix E is in column echelon form the function fstair computes according to the wishes of the user a unitary transformed pencil QE(sEE-AE)ZE which is more or less similar to the generalized Schur form of the pencil sE-A. The function yields also part of the Kronecker structure of the given pencil.

Q,Z are the unitary matrices used to compute the pencil where E is in column echelon form (see ereduc)

See Also

• quaskro quasi-Kronecker form
• ereduc computes matrix column echelon form by qz transformations