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Orthonormal set

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Assume that is a linearly independent set in a Hilbert space Suppose that is an orthonormal set in satisfying the following property:
for each
(a) Show that for each
(b) Let be the orthonormal set gotten from the Gram-Schmidt procedure applied to . Show that for each , where is a complex number of modulus 1.
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Solution Summary

This solution is comprised of a detailed explanation to answer
(a) Show that for each
(b) Let be the orthonormal set gotten from the Gram-Schmidt procedure applied to . Show that for each , where is a complex number of modulus 1.

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