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About this paper
Dmitriy Kunisky, Xifan Yu
The authors determine the exact sum-of-squares (SoS) degree needed to certify that a product of two n-by-r real matrices cannot equal a fixed matrix A of rank at least r+1, when n>r. They show that degree 2r+2 suffices and degree 2r+1 does not. The tied-factor system XXᵀ=Iₙ has degree 4 under the same encoding.
Summary by alphaXiv.
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