Only positive semi-definite ρ guarantee that ((rho circ {bar {P}}_{k|k-1})) is a valid covariance [26].
The Hessian matrix in (11) is semi-positive definite, which guarantees that almost any equilibrium given by the solution of Equation (7) is stable, as long as condition (10) is not satisfied.
Lyapunov's energy functional based on the derived general governing equations of motion with active damping is used to carry out the stability analysis, where it is shown that the active damping matrix must be positive semi-definite to guarantee the dynamic stability.
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In order to guarantee negative definite, μ is required to be less than 1 in [3].
According to Lemma 1, the matrix must be positive definite, which can be guaranteed by (72).
Rule r3 guarantees that definite and indefinite determiners are always placed at the beginning of an NP, which rules out illegal candidates such as 'cantora a' (or '*singer the').
Actually some of such variables have a very small variance; anyway our optimal double shrinkage estimator of the covariance matrices of the clusters guarantees positive definite estimates also in this situation, stabilizing thus the local Mahalanobis distances that we use in our procedure.
Not definitive, just definite.
In this equation, the free-weighting matrix N and the scalar η indicate the relationship between the terms in our system and guarantee the negative definite of stability criteria.
end{cases} (57) According to [28], the eigenvalues of the matrix (B^{T}B) all lie in the interval ([0,8)). So, to guarantee the positive definite of Q, we should set (gammatau >0). In fact, the scheme (57) is the third case of Algorithm 2 in [17].
