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I was trying to compare the maximum value in DCT dictionary (representing an orthonormal dictionary) of size $N \times N$ to that of another DCT dictionary of size $M \times M$, where $M>N$. I always found that the highest value of $DCT_{M \times M} > DCT_{N \times N}$? Is there any mathematical reason behind it? Can this be generalized for all orthonormal dictionaries?

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  • $\begingroup$ It might help if you say what "orthonormal dictionary " means, and what its "value" is. These are not standard terms. $\endgroup$ – kimchi lover Feb 17 at 13:35
  • $\begingroup$ I meant, the orthogonality property should be maintained. So, $AA^T=A^TA=I$. A good example might be discrete cosine transform, Gabor frame etc. $\endgroup$ – God_Help Feb 18 at 6:12

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