sentences:  Let "G" = "GL"("n",C), the general linear group of invertible "n × n" matrices over the complex numbers.For each matrix "A" in "G", the QR decomposition asserts that there exists a unique unitary matrix "Q" and a unique upper triangular matrix "R" with positive real entries on the main diagonal such that "A" = "QR".Thus "G" is a Zappa–Szép product of the unitary group "U"("n") and the group (say) "K" of upper triangular matrices with positive diagonal entries.