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{title2=$x\otimes y$}
{wiki}

For vectors $x,y$ in a Hilbert space, the rank-one operator $(x\otimes y)z=\langle z,y\rangle x$ has $\|x\otimes y\|_1=\|x\|\|y\|$ and $\operatorname{tr}(x\otimes y)=\langle x,y\rangle$.


Rank-one operator

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 106 / 3 / c / Solution

Rank-one operator ( $x \otimes y$ )

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Rank-one operator (x⊗y)

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