In linear algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection about a plane or hyperplane containing the origin. The Householder transformation was used in a 1958 paper by Alston Scott Householder.[1]
Its analogue over general inner product spaces is the Householder operator.
^Householder, A. S. (1958). "Unitary Triangularization of a Nonsymmetric Matrix" (PDF). Journal of the ACM. 5 (4): 339–342. doi:10.1145/320941.320947. MR 0111128. S2CID 9858625.
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linear algebra, a Householdertransformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a...
(novel), a 1960 novel by Ruth Prawer Jhabvala; basis for the film Householdertransformation, an algorithm in numerical linear algebra Grihastha, the second...
numerical analysis. He is the inventor of the Householdertransformation and of Householder's method. Householder was born in Rockford, Illinois, USA. He received...
computing the QR decomposition, such as the Gram–Schmidt process, Householdertransformations, or Givens rotations. Each has a number of advantages and disadvantages...
Hessenberg matrix by a similarity transformation using Householdertransformations. The following procedure for such a transformation is adapted from A Second...
matrices (the identity matrix is the zeroth Pauli matrix) Householdertransformation (the Householder matrix is built through the identity matrix) Square root...
In linear algebra, linear transformations can be represented by matrices. If T {\displaystyle T} is a linear transformation mapping R n {\displaystyle...
triangular factor, and is a triangular matrix and they are used in the Householdertransformation. A reflector Q {\displaystyle Q} belonging to M n ( R ) {\displaystyle...
Over a real or complex vector space, the Householder operator is also known as the Householdertransformation. Roman 2008, p. 243-244 Methods of Applied...
which must complete to give any useful results (see for example, Householdertransformation). The partial result in this case being the first few vectors...
and is called a rectangular relation or a cross-vector. Dyadics Householdertransformation Norm (mathematics) Ricci calculus Scatter matrix Cartesian product...
known until the QR algorithm was designed in 1961. Combining the Householdertransformation with the LU decomposition results in an algorithm with better...
{i} },} where R {\displaystyle \mathbf {R} } is the so-called Householdertransformation matrix, defined as: R = I − 2 d ^ n d ^ n T ; {\displaystyle \mathbf...
Matrix consimilarity Row equivalence Elementary row operations Householdertransformation Least squares, linear least squares Gram–Schmidt process Woodbury...
definite pencil. Eigenvalue perturbation Frobenius covariant Householdertransformation Jordan normal form List of matrices Matrix decomposition Singular...
algorithms: Gram–Schmidt process HouseholdertransformationHouseholder operator — analogue of Householdertransformation for general inner product spaces...
computing the QR decomposition of a matrix. One advantage over Householdertransformations is that they can easily be parallelised, and another is that...
computing QR factorizations are the Gram–Schmidt process and the Householdertransformation. The QR factorization is often used to solve linear least-squares...
k {\displaystyle A_{k}} is transformed via a small-size Householder similarity transformation to the first column of p ( A k ) {\displaystyle p(A_{k})}...
of Gene Golub and William Kahan published in 1965, which uses Householdertransformations or reflections. In 1970, Golub and Christian Reinsch published...
produces another column of the final transformation matrix V {\displaystyle V} , whereas an iteration of Householder produces another factor in a unitary...
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