Householder reflection
[/ˈhaʊsˌhoʊldər rɪˈflɛkʃən/]
nounpl: Householder reflections
reflexão de Householder
1. A linear transformation in linear algebra that reflects vectors across a hyperplane passing through the origin, commonly used in numerical analysis and matrix computations.
The Householder reflection is an essential technique in QR decomposition algorithms.
A reflexão de Householder é uma técnica essencial em algoritmos de decomposição QR.
2. A specific orthogonal transformation defined by a unit vector, used to zero out elements below the diagonal in matrix computations.
In computational linear algebra, Householder reflections are preferred over Givens rotations for their numerical stability.
Em álgebra linear computacional, as reflexões de Householder são preferidas às rotações de Givens por sua estabilidade numérica.
This is a specialized mathematical term primarily used in academic and professional contexts within engineering, computer science, and mathematics. It is named after Alston Scott Householder and is universally referred to by the same name in both English and Portuguese-speaking countries. The term is rarely encountered outside of higher education and technical fields.
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