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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]
A Householder reflection (or Householder transformation) is a transformation that takes a vector and reflects it about some plane or hyperplane. We can use this operation to calculate the QR factorization of an m-by-n matrix with m ≥ n. Q can be used to reflect a vector in such a way that all coordinates but one disappear.
For dense matrices, the left and right unitary matrices are obtained by a series of Householder reflections alternately applied from the left and right. This is known as Golub-Kahan bidiagonalization.
This is a reflection in the hyperplane perpendicular to v (negating any vector component parallel to v). If v is a unit vector, then Q = I − 2vv T suffices. A Householder reflection is typically used to simultaneously zero the lower part of a column. Any orthogonal matrix of size n × n can be constructed as a product of at most n such ...
Together with a first step using Householder reflections and, if appropriate, QR decomposition, this forms the DGESVD routine for the computation of the singular value decomposition. The QR algorithm can also be implemented in infinite dimensions with corresponding convergence results. [12] [13]
The Missouri Attorney General has offered a plea deal to Stephanie Householder, co-owner of the now-closed Circle of Hope Girls Ranch, to testify against her husband in their upcoming abuse trial ...
In linear algebra, the Householder operator is defined as follows. [1] Let be a finite-dimensional inner product space with inner product , and unit ...
Charged 16 months ago with nearly 100 felony counts of child crimes, Boyd and Stephanie Householder aren’t scheduled for trial until the end of 2023. Trial date set for former owners of Missouri ...