Show that q is an orthogonal matrix

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A Householder matrix, or an elementary reflector, has the form Q = I - 2uuT where u is a unit vector. Show that Q is an orthogonal matrix. (Elementary reflectors are often used in computer programs to produce a QR factorization of a matrix A. If A has linearly independent columns, then left-multiplication by a sequence of elementary reflectors can produce an upper triangular matrix.)

Reference no: EM131074399

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