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Exercise 4.1.8

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If $A$ is orthogonal, then $a_{i}$ are orthogonal to each other. Also we have $A A^{T} = Q Q^{T} = I$ , so $A A^{T} x = x$ . The $n$ pieces in $A A^{T} x$ are orthogonal vectors to each other. We can treat $a_{i}$ as basis functions. Since $a_{i}^{T} a_{i} = 1$ , that’s equivalent to normalize the $b_{k}$ in Fourier matrix $F$ , so we have $F Ω = I$

niuers

2020-03-20 00:00

Exercise 4.1.8

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