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
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.
Famous quotes containing the word householder:
“In relation to God, we are like a thief who has burgled the house of a kindly householder and been allowed to keep some of the gold. From the point of view of the lawful owner this gold is a gift; From the point of view of the burglar it is a theft. He must go and give it back. It is the same with our existence. We have stolen a little of God’s being to make it ours. God has made us a gift of it. But we have stolen it. We must return it.”
—Simone Weil (1909–1943)