In linear algebra, the Householder operator is defined as follows.[1] Let be a finite-dimensional inner product space with inner product and unit vector . Then
is defined by
This operator reflects the vector across a plane given by the normal vector .[2]
It is also common to choose a non-unit vector , and normalize it directly in the Householder operator's expression:[3]
^Roman 2008, p. 243-244
^Methods of Applied Mathematics for Engineers and Scientist. Cambridge University Press. pp. Section E.4.11. ISBN 9781107244467.
^Roman 2008, p. 244
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