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MAT QR OF A TO Q,R
makes the QR factorization of m*n A (m>=n) by Householder transformations
(Algorithm 5.2.1 in Golub, van Loan: Matrix Computations, 1989).
Q will be m*m orthogonal matrix and R m*n upper triangular so that
A=Q*R.

MAT QRP OF A TO Q,R,tol
makes the Householder QR with column pivoting of m*n A
(Algorithm 5.4.1 in Golub, van Loan: Matrix Computations, 1989).
The permutation of columns is saved in QR_PERM.M so that
PERM2(A,QR_PERM.M)=Q*R.
tol gives the lowest admitted pivot value for rank determination.
Default is tol=1e-15.
r=rank(A) and an indicator vector of the optimal permutation is saved
in QR_SEL.M .
Then
MAT A2=SUB(A,*,QR_SEL.M)
gives m*r A2 as a basis of the column space of A.

  D = More information on matrix decompositions