Orthogonal Bases and the QRAlgorithm

  title={Orthogonal Bases and the QRAlgorithm},
  author={Peter J. Olver},
Throughout, we work in the Euclidean vector space V = R, the space of column vectors with n real entries. As inner product, we will only use the dot product v ·w = v w and corresponding Euclidean norm ‖v ‖ = √v · v . Two vectors v,w ∈ V are called orthogonal if their inner product vanishes: v ·w = 0. In the case of vectors in Euclidean space, orthogonality under the dot product means that they meet at a right angle. A particularly important configuration is when V admits a basis consisting of… CONTINUE READING