Kunze Linear Algebra · Problem 8.2.11

Inner Product Spaces

Mathematics — Methods · orthonormal-bases-inner-products

Problem

Let VV be a finite-dimensional inner product space, and let {α1,…,αn}\{\alpha_1, \ldots, \alpha_n\} be an orthonormal basis for VV. Show that for any vectors α\alpha, β\beta in VV (α∣β)=∑k=1n(α∣αk)(β∣αk)‾.(\alpha|\beta) = \sum_{k=1}^n (\alpha|\alpha_k)\overline{(\beta|\alpha_k)}.

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