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Show that a n times n Householder matrix H = I - 2vv^T/v^T v has an eigenvalue of 1 with multiplicity n - 1 and

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Show that a n times n Householder matrix H = I - 2vv^T/v^T v has an eigenvalue of 1 with multiplicity n - 1 and an eigenvalue of -1 with multiplicity 1

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