       Re: full QR decomposition

• To: mathgroup at smc.vnet.net
• Subject: [mg51704] Re: full QR decomposition
• From: koopman at sfu.ca (Ray Koopman)
• Date: Fri, 29 Oct 2004 03:40:28 -0400 (EDT)
• References: <clprf3\$a4b\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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:= 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//InputForm= 8.881784197001252*^-16

```

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