fstair — computes pencil column echelon form by qz transformations
[AE,EE,QE,ZE,blcks,muk,nuk,muk0,nuk0,mnei]=fstair(A,E,Q,Z,stair,rk,tol)
m x n matrix with real entries.
real positive scalar.
column echelon form matrix
m x m unitary matrix
n x n unitary matrix
vector of indexes (see ereduc)
integer, estimated rank of the matrix
m x n matrix with real entries.
column echelon form matrix
m x m unitary matrix
n x n unitary matrix
is the number of submatrices having full row rank >= 0 detected in matrix A.
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)
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)
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)
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)
integer array of dimension (4). mnei(1) = row dimension of sE(eps)-A(eps)
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)