This is a decent derivation, if a little verbose, but I find myself doubting the disclaimer at the top:
> Disclaimer: no AI was used to write this. Any errors, awkward sentences, and weird tangents are 100% organic, free-range, and human-made.
If you're writing by hand and trying to avoid accusations of AI-generated content, it's really easy not to write bulleted lists where each item starts with a boldface summary like "A clean bijection in the middle." Or drive home a point with such pithy italicized mottos as "The complexity was never in the map. It was in the basis." If you didn't use AI in the writing here, you have trained yourself very well to write like an LLM.
Im not trying anything. I just put as a joke. Im using AI to learn, but I wrote the structure and the references, and remodeled some parts with AI, yes, but I wrote the base input text by hand, in the sense AI would not be needed, but it helps me as English is not my first language.
Slight mistake in equation (1) (or maybe it's supposed to be a narrative decision?), the inner product of Av_i with itself should end up being s_i^2 and not 1. The vectors u_i are orthonormal, but Av_i = s_i u_i, not just u_i.
These day's I'm super-into information theory and entropy, so I liked the connection made at the end. I'm a visual person, and I found this schematic of SVD on the wikipedia page very insightful [1].
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[ 0.23 ms ] story [ 21.5 ms ] thread> Disclaimer: no AI was used to write this. Any errors, awkward sentences, and weird tangents are 100% organic, free-range, and human-made.
If you're writing by hand and trying to avoid accusations of AI-generated content, it's really easy not to write bulleted lists where each item starts with a boldface summary like "A clean bijection in the middle." Or drive home a point with such pithy italicized mottos as "The complexity was never in the map. It was in the basis." If you didn't use AI in the writing here, you have trained yourself very well to write like an LLM.
[1]: https://en.wikipedia.org/wiki/Singular_value_decomposition#/...