Transform NumPy QR to R[i,i] > 0 Suppose D is a diagonal matrix containing +1 and-1 entries. Then (Q D)T(Q D) = Dr QT Q D = DI D = D2-1 so Q D has orthonormal columns . DR is right triangular. Given a QR factorization that may not satisfy R[i,i] > 0, construct a diagonal matrix D such that is a valid QR factorization that satisfies Rhat[i,i] 0 def positive qr(Q, R): """Transform Q@R to Qhat @ Rhat such that Rhat[i,i] > 0."" dnp.negative.identity(len(R)) Rhat = d * R return Qhat, Rhat ghat, Rhat = positive-ar(Q, R) Transform NumPy QR to R[i,i] > 0 Suppose D is a diagonal matrix containing +1 and-1 entries. Then (Q D)T(Q D) = Dr QT Q D = DI D = D2-1 so Q D has orthonormal columns . DR is right triangular. Given a QR factorization that may not satisfy R[i,i] > 0, construct a diagonal matrix D such that is a valid QR factorization that satisfies Rhat[i,i] 0 def positive qr(Q, R): """Transform Q@R to Qhat @ Rhat such that Rhat[i,i] > 0."" dnp.negative.identity(len(R)) Rhat = d * R return Qhat, Rhat ghat, Rhat = positive-ar(Q, R)