8. Let x be the first column of A and let Show that if Q, is the Householder matrix given by Problem 6, then Q,A is a matrix with the block form Q.A = where A, is (m – 1)X(n – 1). If we repeat Problem 8 on the matrix A, we use a Householder matrix P; such that PA, =. o A] where A, is (m - 2)X(n – 2).

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
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8. Let x be the first column of A and let
Show that if Q, is the Householder matrix given by Problem 6, then Q,A is a matrix
with the block form
Q.A =
where A, is (m – 1)X(n – 1).
If we repeat Problem 8 on the matrix A, we use a Householder matrix P; such that
PA, =.
o A]
where A, is (m - 2)X(n – 2).
Transcribed Image Text:8. Let x be the first column of A and let Show that if Q, is the Householder matrix given by Problem 6, then Q,A is a matrix with the block form Q.A = where A, is (m – 1)X(n – 1). If we repeat Problem 8 on the matrix A, we use a Householder matrix P; such that PA, =. o A] where A, is (m - 2)X(n – 2).
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