Householder operator

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In Linear algebra, define the Householder operator as follows.

Let be a finite dimensional inner product space with unit vector Then, the Householder operator is an operator defined by

where is the inner product over . This operator reflects the vector across a plane given by the normal vector .[1]

Over a real vector space, the Householder operator is also known as the Householder transformation.

The Householder operator has numerous properties such as linearity, being self-adjoint, and is a unitary or orthogonal operator on V.


  1. ^ Methods of Applied Mathematics for Engineers and Scientist. Cambridge University Press. pp. Section E.4.11. ISBN 9781107244467.