**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Householder operator

Summary

In linear algebra, the Householder operator is defined as follows. Let V, be a finite-dimensional inner product space with inner product \langle \cdot, \cdot \rangle and unit vector u\in V. Then
: H_u : V \to V,
is defined by
: H_u(x) = x - 2,\langle x,u \rangle,u,.
This operator reflects the vector x across a plane given by the normal vector u.
It is also common to choose a non-unit vector q \in V, and normalize it directly in the Householder operator's expression:
:H_q \left ( x \right ) = x - 2, \frac{\langle x, q \rangle}{\langle q, q \rangle}, q ,.
Properties
The Householder operator satisfies the following properties:

- It is linear; if V is a vector space over a field K, then :\forall \left ( \lambda, \mu \right ) \in K^2, , \forall \left ( x, y \right ) \in V^2, , H_q \left ( \lambda x + \mu y \righ

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related publications

Related people

Related units

Related lectures

No results

No results

No results

No results

Related concepts

No results

Related courses

No results