Question: (a) Write down the Householder matrices corresponding to the following unit vectors: (b) Find all vectors fixed by a Householder matrix, i.e., Hv = v

(a) Write down the Householder matrices corresponding to the following unit vectors:


T 34 (i) (1,0), (ii) (3, 4), (ii) (0,1,0), (iv) (20,-2) T


(b) Find all vectors fixed by a Householder matrix, i.e., Hv = v — first for the matrices in part (a), and then in general. 


(c) Is a Householder matrix a proper or improper orthogonal matrix?

T 34 (i) (1,0), (ii) (3, 4), (ii) (0,1,0), (iv) (20,-2) T

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ANSWER a The Householder matrix corresponding to a unit vector u is given by H I 2uuT where I is the ... View full answer

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