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Math Help - Orthonormal

  1. #1
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    Unhappy Orthonormal

    Could anyone help me with one direction proof of this problem please?

    Suppose that beta and gamma are ordered bases for an n-dimensional real (complex) inner product space V. Prove that if Q is an orthogonal (unitary) n by n matrix that changes gamma-coordinates into beta-coordinates, then beta is orthonormal if and only if gamma is orthonormal.
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  2. #2
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    Opalg's Avatar
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    Hint: for vectors x, y in V, \langle Qx,Qy\rangle = \langle Q^*Qx,y\rangle = \langle x,y\rangle.
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