A type of QR Decomposition

[skyhr]

Hello,

I am reading a research paper in which a certain algorithm involves the QR Decomposition. This QR decomposition is different from the Matlab version: In Matlab, [B,C] = qr(Matrix of size n x u) returns B => u x u orthogonal matrix and C => n x u upper triangular matrix. The QR Decomposition in the research paper, however, is different. Here, [B,C] = qr(Matrix of size n x u) returns B => n x u matrix of orthogonal columns and C => u x u sized upper triangular matrix.

How can I use Matlab to produce the second type of QR decomp?

Thanks

 

[daon]

This makes no sense, an upper triangular matrix is square by definition.

Either way, any upper triangular matrix can be represented by a product of elementary (upper triangular) matricies. Multiply one matrix by the elementary matricies of the other and I suppose you'll get the result.

 

[skyhr]

I know it doesn't make much sense, but it is what Matlab gives me:

=== Matlab ===
>> a = magic(4);
>> a,1)=''

a =

2 3 13
11 10 8
7 6 12
14 15 1

>> [b,c]=qr(a)

b =

-0.1040 0.5061 -0.8265 -0.2236
-0.5719 -0.4709 -0.0349 -0.6708
-0.3639 -0.4817 -0.4307 0.6708
-0.7278 0.5386 0.3609 0.2236


c =

-19.2354 -19.1314 -11.0214
0 1.9973 -2.4303
0 0 -15.8311
0 0 0


==== End Matlab ===

B should be n x u and c should be square matrix, but Matlab doesn't give me this.

How can I fix this?

Thanks