A subset {v_1, ..., v_k} of a vector space V, with the inner product 〈, 〉, is called orthonormal if 〈v_i, v_j〉 = 0 when i!=j. That is, the vectors are mutually perpendicular. Moreover, they are all required to have length one: 〈v_i, v_i〉 = 1. An orthonormal set must be linearly independent, and so it is a vector basis for the space it spans. Such a basis is called an orthonormal basis.

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