ereduc - computes matrix column echelon form by qz transformations

Calling Sequence

[E,Q,Z [,stair [,rk]]]=ereduc(X,tol)

Parameters

• X : 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,
  • * ISTAIR(i) = + j if the boundary element E(i,j) is a corner point.
  • * ISTAIR(i) = - j if the boundary element E(i,j) is not a corner point.

  (i=1,...,M)

• rk : integer, estimated rank of the matrix

Description

Given an m x n matrix X (not necessarily regular) the function ereduc computes a unitary transformed matrix E=Q*X*Z which is in column echelon form (trapezoidal form). Furthermore the rank of matrix X is determined.

Examples

X=[1 2 3;4 5 6]
[E,Q,Z ,stair ,rk]=ereduc(X,1.d-15)
 
  

See Also

fstair ,  

Author

Th.G.J. Beelen (Philips Glass Eindhoven). SLICOT