Numerical linear algebra

Householder operator

In linear algebra, the Householder operator is defined as follows. 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 . It is also common to choose a non-unit vector , and normalize it directly in the Householder operator's expression (Wikipedia).

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Related pages

Orthogonal matrix | Householder transformation | Operator (mathematics) | Vector space | Unit vector | Linear algebra | Inner product space | Self-adjoint | Unitary matrix