# On Certain Positivity Classes of Operators

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### "On Certain Positivity Classes of Op..." refers background in this paper

...For matrices, it is known that any matrix in the subset r(A,B) is invertible if and only if BA−1 is a P-matrix [8]....

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...If s > ρ(B), thenA is invertible, and in this caseA−1 ≥ 0 [2]....

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...HenceA is a P-matrix....

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...This result is quite well known in the theory of linear complementarity problems [2]....

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...It is well known that the linear complementarity problem de ned by a matrix A has a unique solution if and only if A is a P-matrix [4]....

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### "On Certain Positivity Classes of Op..." refers background in this paper

...Fiedler and Ptak [5] have shown that A is a P-matrix if and only if A does not reverse the sign of any non-zero vector....

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...AmatrixA ∈ Rn×n is said to be a P-matrix [5] if all its principal minors are positive....

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...A real square matrix A is called a P-matrix if all its principal minors are positive....

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...P-operators As mentioned earlier, a square matrix A is called a P-matrix if all its principal minors are positive....

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...More importantly, such a matrix is, in fact, a P-matrix....

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