<aside> 💡 An orthonormal set of vectors of an inner product space $V$ is an orthogonal set of vectors such that the norm of each vector of the set is 1.
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<aside> 💡 An orthonormal basis is an orthonormal set of vectors which forms a basis.
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<aside> 💡 Equivalently: An orthonormal basis is an orthogonal basis where the norm of each vector is 1.
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<aside> 💡 Equivalently: An orthonormal basis is a maximal orthonormal set.
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Example: The standard basis w.r.t the usual inner product forms an orthonormal basis.
Let $V$ be an inner product space, if $\Gamma = \{v_1,v_2,....,v_n\}$ is an orthogonal set of vectors, then we can obtain an orthonormal set of vectors $\beta$ from $\Gamma$ by:
<aside> 💡 $\beta = \{ \frac {v_1} {||v_1||}, \frac {v_2} {||v_2||},......,\frac {v_n} {||v_n||} \}$
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