# QR decomposition

I have a matrix which is "almost" like an upper triangular just that the last row has non zero elements. And I want to perform the QR decomposition on that matrix.

Does anyone know the "name" of such a matrix? And also since I don't want to use the built in matlab QR function for such a matrix, can anyone suggest a better algorithm for me to use?

• Have you considered the Cholesky decomposition, please? Or LU decomposition? I use R rather than Matlab, but I believe that those may be effective for your problem. Would you happen to have a small numeric example, by any chance? Sep 28 '15 at 3:06
• The main idea is to observe the sensitivity of the diagonal elements. The original matrix was a full matrix where I used the built in matlab function QR to decompose it. But now I have purturbed (R+E) the R upper triangular matrix of the decomposition with E( E is an NxN matrix with its elements all zeros except at the last row where it has non zero elements) The shape of (R+E) is almost like the Upper triangular matrix R since it has zeros below its diagonal except it's last row. Sep 28 '15 at 10:58
• I am expected to take the QR decomposition of this new matrix (R+E) in other to observe how sensitive the diagonal elements of R with respect to (E) is. I no longer want to use the matlab QR built function since this new matrix is (almost upper triangular except at the last row where you have non zero elements). I do have numeric examples but since I'm new here, I don't know how to type in matrices. Sep 28 '15 at 10:58
• This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post - you can always comment on your own posts, and once you have sufficient reputation you will be able to comment on any post. Sep 28 '15 at 19:59
• @user1544953 Cholesky only works for SPD matrices. I doubt that the matrix here is symmetric. Nov 20 '15 at 2:56