Norm of linear combination of orthonormal vectors. Suppose a1, . . . , ak are orthonormal n-vectors, and x = β1a1 + ··· + βkak, where β1, ..., βk are scalars. Express ‖x‖ in terms of β = (β1, ..., βk).
Added by Seth S.
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Step 1:** Express the norm of the vector x as the sum of the norms of the individual components: \(\|x\| = \| \beta_1 a_1 + \beta_2 a_2 + \ldots + \beta_k a_k \| \) ** Show more…
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