Question: If P is an n 1 matrix such that PT P = 1, then H = I - 2PPT is called the corresponding Householder

If P is an n × 1 matrix such that PT P = 1, then H = I - 2PPT is called the corresponding Householder matrix (named after the American mathematician A. S. Householder).
Prove that if H is any Householder matrix, then H = HT and HTH = I.

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