Orderings on semirings and completely positive matrices

Mohindru, Preeti; Pereira, Rajesh

doi:10.1080/03081087.2015.1059405

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Definition 113 (Arithmetic Geometric Property) a Commutative...1

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2016

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Cited by 4 publications

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“…This definition agrees with [22] where these concepts were defined for matrices over general semirings. If L has the unique square root property, then positive semidefiniteness and complete positivity coincide.…”

Section: Definition 113 (Arithmetic Geometric Property) a Commutative...supporting

confidence: 75%

The DJL Conjecture for CP Matrices over Special Inclines

Mohindru

Pereira

2016

Communications in Algebra

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Drew, Johnson and Loewy conjectured that for $n \geq 4$, the CP-rank of every $n \times n$ completely positive real matrix is at most $\left[n^{2}/4\right]$. While this conjecture is false for completely positive real matrices, we show that this conjecture is true for $n \times n$ completely positive matrices over certain special types of inclines. In addition, we prove an incline version of Markham's theorems which gives sufficient conditions for completely positive matrices over special inclines to have triangular factorizations

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Section: Definition 113 (Arithmetic Geometric Property) a Commutative...supporting

confidence: 75%