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Re: full QR decomposition


Jan Schmedes <schmedes at rz.uni-potsdam.de> wrote in message 
news:<clprf3$a4b$1 at smc.vnet.net>...
> i have the following problem. For a given a NxM (e.g. 3000x600) matrix A i
> get a matrix Q (MxN) and R (MxM) after the QRDecomposition. But i would
> like to get the full decomposition with a matrix QF (NxN) and RF (NxM) where
> RF contains only zero lines below the line with index M. I'm especially
> interrested in the last N-M lines in QF which create the zero lines in RF.
> At the moment i use QRDecomposition and append then N-M random lines to the
> matrix Q. With this new matrix i go into the routine GramSchmidt and extract
> the last N-M lines from the result. But this is very slow and i'm not sure if
> it will always work? Are there any suggestions or hints?

In[1]:= a = Table[Random[],{30},{6}];
        q = First@QRDecomposition@a;
        qf = Join[q,First@QRDecomposition@Transpose@NullSpace@q];
        Max at Abs[qf.Transpose@qf-IdentityMatrix@30] // InputForm

Out[4]//InputForm= 8.881784197001252*^-16


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