Nuclear Norm Under Tensor Kronecker Products

01/20/2020

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by   Robert Cochrane, et al.

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Derksen proved that the spectral norm is multiplicative with respect to vertical tensor products (also known as tensor Kronecker products). We will use this result to show that the nuclear norm and other norms of interest are also multiplicative with respect to vertical tensor products. Finally, we prove an analogue of Strassen's direct sum conjecture for the nuclear norm.