A concise proof to the spectral and nuclear norm bounds through tensor partitions

A concise proof to the spectral and nuclear norm bounds through tensor partitions

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On estimations of the lower and upper bounds for the spectral and nuclear norm of a tensor, Li established neat bounds for the two norms based on regular tensor partitions, and proposed a conjecture for the same bounds to be hold based on general tensor partitions [Z.Li, Bounds on the spectral norm and the nuclear norm michael harris sunglasses of a tensor based on tensor partition, SIAM J.Matrix Anal.Appl.

, 37 (2016), pp.1440-1452].Later, Chen and Li provided koip share price a solution to the conjecture [Chen B., Li Z.

, On the tensor spectral p-norm and its dual norm via partitions].In this short paper, we present a concise and different proof for the validity of the conjecture, which also offers a new and simpler proof to the bounds of the spectral and nuclear norms established by Li for regular tensor partitions.Two numerical examples are provided to illustrate tightness of these bounds.