Householder matrix
In linear algebra, a Householder transformation (also known as 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 introduced in 1958 by Alston Scott Householder.
Its analogue over general inner product spaces is the Householder operator.
The reflection hyperplane can be defined by a unit vector (a vector with length ) which is orthogonal to the hyperplane. The reflection of a point about this hyperplane is the linear transformation:
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