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In linear algebra, a Householder transformation ... (1963). "The reduction of an arbitrary real square matrix to tridiagonal form using similarity transformations".
In mathematics, and more specifically in numerical analysis, Householder's methods are a class of root-finding algorithms that are used for functions of one real variable with continuous derivatives up to some order d + 1. Each of these methods is characterized by the number d, which is known as the order of the method.
A tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix. [2] In particular, a tridiagonal matrix is a direct sum of p 1-by-1 and q 2-by-2 matrices such that p + q/2 = n — the dimension of the tridiagonal.
A square matrix is said to be in lower Hessenberg form or to be a lower Hessenberg matrix if its transpose is an upper Hessenberg matrix or equivalently if , = for all , with > +. A lower Hessenberg matrix is called unreduced if all superdiagonal entries are nonzero, i.e. if a i , i + 1 ≠ 0 {\displaystyle a_{i,i+1}\neq 0} for all i ∈ { 1 ...
A Householder reflection (or Householder transformation) is a transformation that takes a vector and reflects it about some plane or hyperplane. We can use this operation to calculate the QR factorization of an m-by-n matrix with m ≥ n. Q can be used to reflect a vector in such a way that all coordinates but one disappear.
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Alston Scott Householder (5 May 1904 – 4 July 1993) was an American mathematician who specialized in mathematical biology and numerical analysis. He is the inventor of the Householder transformation and of Householder's method .
Some say the open-concept home can be overstimulating and take a toll on mental health. (Yahoo Illustration: Alex Cochran for Yahoo News, photos: Getty Images) (Yahoo Illustration: Alex Cochran ...