# [R] QR Decompositon and qr.qty

From: Sebastian Bauer <Sebastian.Bauer_at_charite.de>
Date: Tue, 15 May 2007 15:20:00 +0100

I do not have much knowledge about linear algebra but currently I need to understand what the function qr.qty is actually doing. The documentation states that it calculates t(Q) %*% y via a previously performed QR matrix decomposition.

In order to do that, I tried following basic example:

[,1] [,2] [,3] [,4]
[1,] -1 -2 -1 -2
[2,] -4 -5 -1 -2
[3,] 3 4 1 2
[4,] -2 -3 -1 -2

As far as I understood the documentation a call such as

t(qr.Q(qr(m)))%*%matrix(c(1,2,3,4,2,3,4,5,1,1,1,1,2,2,2,2),nrow=4)

should produce the same result, but this produces a 3 by 4 rather than a four by four matrix as t(qr.Q(qr(m))) has only three rows.

[,1] [,2] [,3] [,4]
[1,] -1 -2 -1 -2
[2,] -4 -5 -1 -2
[3,] 3 4 1 2

So the last line is missing. Any hints how R adds the last line would be appreciated.

Regards,
Sebastian

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