QR-Decomposition from the Statistical Point of View
Hilmar Drygas · 2008
We denote by span{z1, . . . , zr} the linear subspace spanned by the vectors z1, . . . , zr of the vector-space V . For a matrix A we denote the range of the matrix A by im(A) and its rank by r(A). A g-inverse of A is denoted A− and the Moore-Penrose of A is denoted by A+. PL denotes the orthogonal projection into the linear subspace L of the vector-space V . It should be noted that the model (1) is the most general linear model. Further, (1) is understood with respect to a general inner product, i.e.,