CentralNotice QR decomposition From Wikipedia, the free encyclopedia Jump to: navigation , search 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 eigenvalue 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 . [ 1 ] 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 . [ 1 ] 1 History 2 Definitions 2.1 Squar...