Important: The linalg package has been deprecated. Use the superseding packages, LinearAlgebra and VectorCalculus, instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The routine QRdecomp computes the QR decomposition of the matrix A.

For matrices of floating-point entries, the numerically stable Householder-transformations are used.  For symbolic computation, the Gram-Schmidt process is applied.

The result is an upper triangular matrix R.  The orthonormal (unitary) factor Q is passed back to the Q parameter.

The default factorization is the full QR where R will have the same dimension as A.  Q will be a full rank square matrix whose first n columns span the column space of A and whose last m-n columns span the null space of A.

If the (optional) fullspan arg is set to false, a Q1R1 factorization will be given where the Q1 factor will have the same dimension as A and, assuming A has full column rank, the columns of Q will span the column space of A. The R factor will be square and agree in dimension with Q.  The default for fullspan is true.

If A is an n by n matrix then .

If A contains complex entries, the Q factor will be unitary.

The QR factorization can be used to generate a least squares solution to an overdetermined system of linear equations.  If , and  then  can be solved through backsubstitution.

The command with(linalg,QRdecomp) allows the use of the abbreviated form of this command.

Warning, unable to find a provably non-zero pivot

Warning, unable to find a provably non-zero pivot