What is the tensor power series of a vector?

Asked Mar 09 '22 at 19:01

Active Mar 10 '22 at 00:03

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In this Wikipedia article https://en.m.wikipedia.org/wiki/Jet_(mathematics) there’s Taylor’s theorem for functions $f: \mathbb{R}^m \to \mathbb{R}^n$ where $f(x)=\sum_{n\in \mathbb{N}} D^n f(x_0) (x-x_0)^{\otimes n} /n!$.

What does this tensor product mean here and where can I learn more about it?

If it’s just the normal krownecker/tensor product, then how do they sum to a vector?

edited Mar 10 '22 at 00:03

asked Mar 09 '22 at 19:01

Lave Cave

1,257

Does this answer your question? Kronecker Products and Powers notation – Momo Mar 09 '22 at 19:29
See In multivariate Taylor expansion formula, what is meant by $(x−a)^k$?. Sure, there, they didn't use the tensor product symbol, but the meaning is exactly the same (also in that answer I use the notation $d^nf(a)$, which is the same thing as $D^nf(a)$). Or a similar answer in more detail. – peek-a-boo Mar 09 '22 at 22:27

What is the tensor power series of a vector?

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