In this paper, we prove that all H$^+$(Z$^+$)-eigenvalues of each principalsub-tensor of a strictly semi-positive tensor are positive. We define two newconstants associated with H$^+$(Z$^+$)eigenvalues of a strictly semi-positivetensor. With the help of these two constants, we establish upper bounds of animportant quantity whose positivity is a necessary and sufficient condition fora general tensor to be a strictly semi-positive tensor. The monotonicity andboundedness of such a quantity are established too. Furthermore, we presentglobal error bound analysis for a class of the nonlinear complementarityproblem defined by a strictly semi-positive tensor.
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