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11 Nov 2019
Please help on these
Let u be a nonzero vector in Rn. Let H = I - 2p uuT where p = 1/(uTu). H is called a Householder matrix. Prove that H is orthogonal. Let x be an arbitrary vector in Rn and let y = Ax. Prove that ||x|| = \\y\\ if and only if A is orthogonal. Here ||.|| is the usual Euclidean norm. Let Q1 , Q2 be two n x n orthogonal matrices. Prove or disprove that Q = Q1Q2 is orthogonal.
Please help on these
Let u be a nonzero vector in Rn. Let H = I - 2p uuT where p = 1/(uTu). H is called a Householder matrix. Prove that H is orthogonal. Let x be an arbitrary vector in Rn and let y = Ax. Prove that ||x|| = \\y\\ if and only if A is orthogonal. Here ||.|| is the usual Euclidean norm. Let Q1 , Q2 be two n x n orthogonal matrices. Prove or disprove that Q = Q1Q2 is orthogonal.
Irving HeathcoteLv2
12 May 2019