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## Q-R decomposition with positive diagonals of R Matrix

version 1.2.0.0 (363 Bytes) by Gnaneswar Nadh satapathi

### Gnaneswar Nadh satapathi (view profile)

Q-R decomposition with positive diagonals for a square random matrix

Updated 24 Feb 2015

In linear algebra, a QR decomposition (also called a QR factorization) of a matrix is a decomposition of a matrix A into a product A = QR of an orthogonal matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares problem, and is the basis for a particular eigen value algorithm, the QR algorithm. If A has n linearly independent columns, then the first n columns of Q form an orthonormal basis for the column space of A. More specifically, the first k columns of Q form an orthonormal basis for the span of the first k columns of A for any 1 ≤ k ≤ n. The fact that any column k of A only depends on the first k columns of Q is responsible for the triangular form of R.

### Cite As

Gnaneswar Nadh satapathi (2020). Q-R decomposition with positive diagonals of R Matrix (https://www.mathworks.com/matlabcentral/fileexchange/49807-q-r-decomposition-with-positive-diagonals-of-r-matrix), MATLAB Central File Exchange. Retrieved .

Justin Michael

### Justin Michael (view profile)

If goal is to determine a QR decomposition that enforces positive diagonals (making solution unique), I suspect the following is a much simpler approach:

[Q,R] = qr(A);
D = diag(sign(diag(R)));
Qunique = Q*D;
Runique = D*R;