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Spatial transformations? Take a look at the complex matrices in Fourier transforms with nth roots of unity as its elements. The values are cyclic, and do not re
by zkmon 1y ago
Spatial transformations? Take a look at the complex matrices in Fourier transforms with nth roots of unity as its elements. The values are cyclic, and do not represent points in an n-D space of Euclidean coordinates.
- blackbear_ 1y agoYes; I wrote linear transformation on purpose not to remain constrained on spatial or geometric interpretations. The (discrete) Fourier transform is also a linear transformation, which is why the initial effort of thinking abstractly in terms of vector spaces and transformations between them pays lots of dividends when it's time to understand more advanced topics such as the DFT, which is "just" a change of basis.