Talk:Tensor reshaping

Wrong content

The article defines a "projection"

${\displaystyle {\begin{aligned}\Pi$ :&V_{1}\otimes V2\to V_{1}\\&\Pi (x\otimes y)=x\end{aligned}}.}

Such a mapping cannot exist. In fact, as $(2x)\otimes y=x\otimes (2y),$ this would imply $x=2x,$ even for a nonzero $x.$ D.Lazard (talk) 10:12, 19 January 2020 (UTC)

What you state is correct. The correct way to define it is to choose any element from the preimage of $\otimes :V_{1}\times \cdots \times V_{n}\to V_{1}\otimes \cdots \otimes V_{n}$, then take the appropriate coordinate projections $\Pi _{S_{i}}$ and then tensor them. A reference to Landsberg, Tensors: Geometry and Applications, 2012 could be added as a source. Ntheazk (talk) 21:53, 28 January 2020 (UTC)