| http://www.w3.org/ns/prov#value | - u = x ??? ??? x ??? e 1 Then , P . x = x - u H . ( x ??? ??? x ??? e 1 ) T . x = x - 2 u . ( ( ??? x ??? 2 ??? ??? x ??? x 1 ) T 2 ??? x ??? 2 ??? 2 ??? x ??? x 1 = x - . u = ??? ??? x ??? e 1 Similarly , ( 25 ) x T ??? P = ??? ??? x ??? e i T ( 26 ) Thus, the Householder matrix acts on a given vector to zero all its elements except the first one.
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