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by wrycoder
1466 days ago
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LA is about vectors and rotations and stretches of vectors, which is what happens when you multiply a vector by a matrix. That’s what you will be visualizing. Try the Kahn videos, then watch the 3B1B videos, which are very visual, but somewhat advanced. Or, watch both of them several times in parallel. |
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Elsewhere, I've discovered that this poster is going into image processing, which is likely "signals and systems" linear algebra.
In signals and systems, your vectors can have infinite dimension, and these infinite-dimension vectors Fourier-transform into other infinite dimension vectors under a new basis.
Any field with more than "3 dimension" vectors / matricies is very difficult to visualize geometrically. Trying to do so is counter-productive to the understanding of the field. This geometric interpretation is really useful in graphics programming / 3d animation however.
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Or perhaps a more concrete example... your "visualize the matrix in X dimensions" advice just doesn't cut it if you're dealing with an 8x8 matrix JPEG DCT coefficient matrix (https://en.wikipedia.org/wiki/JPEG#Discrete_cosine_transform), unless you can imagine 8-diemsional space in your brain.
On the other hand, imagining the 8x8 matrix as 64 linearly-independent "Basis" to your 64-dimension discrete signal is... easier. (Well... for a definition of easier at least). And the transform from time domain into Fourier domain is a transformation in basis that contains the same information.