  In this paper, we prove that all H$^+$(Z$^+$)-eigenvalues of each principal
sub-tensor of a strictly semi-positive tensor are positive. We define two new
constants associated with H$^+$(Z$^+$)eigenvalues of a strictly semi-positive
tensor. With the help of these two constants, we establish upper bounds of an
important quantity whose positivity is a necessary and sufficient condition for
a general tensor to be a strictly semi-positive tensor. The monotonicity and
boundedness of such a quantity are established too. Furthermore, we present
global error bound analysis for a class of the nonlinear complementarity
problem defined by a strictly semi-positive tensor.
