Bounds on Dimension Reduction in the Nuclear Norm

arXiv: Metric Geometry, 2019.

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Abstract:

$ newcommand{schs}{scriptstyle{mathsf{S}}_1} $For all $n ge 1$, we give an explicit construction of $m times m$ matrices $A_1,ldots,A_n$ with $m = 2^{lfloor n/2 rfloor}$ such that for any $d$ and $d times d$ matrices $Au0027_1,ldots,Au0027_n$ that satisfy [ |Au0027_i-Au0027_j|_{schs} ,leq, |A_i-A_j|_{schs},leq, (1+delta) |Au0027_i-Au0027_...More

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