Let ##X, Y## be vector spaces, say over ##\mathbb{R}##. These spaces need not be finite-dimensional.
Let ##T## denote the space of bilinear maps ##b:X\times Y\to \mathbb{R}##, and let ##T^*## stand for the corresponding algebraic dual space. By definition, ##x\otimes y## is the element of ##T^*## defined by ##(x\otimes y)(b):=b(x,y).##
Thus, we have a mapping ##\psi:X\times Y\to T^*## given by ##\psi(x,y)=x\otimes y.##
We define the tensor product of the spaces as ##X\otimes Y:=\text{span}\,\psi(X\times Y)##
Then I realized I flipped your ##T## and ##T^*## in my head as I'm used to attaching a star to the space of maps of vectors.
| # | Наименование новости | Тональность | Информативность | Дата публикации |
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| 1 | 0 | 0 | 25-05-2026 | |
| 2 | 0 | 0 | 29-04-2026 | |
| 3 | 0 | 0 | 19-04-2026 | |
| 4 | 0 | 0 | 14-10-2026 | |
| 5 | 0 | 0 | 14-10-2026 | |
| 6 | 0 | 0 | 14-10-2026 | |
| 7 | 0 | 0 | 24-11-2016 | |
| 8 | 0 | 0 | 24-11-2016 | |
| 9 | 0 | 0 | 24-11-2016 | |
| 10 | Best visualization of SO(3) | 0 | 35 | 11-10-2026 |