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A Characterization of Nonnegativity Relative to Proper Cones
Indian Journal of Pure and Applied Mathematics ( IF 0.7 ) Pub Date : 2020-10-06 , DOI: 10.1007/s13226-020-0442-4
Chandrashekaran Arumugasamy , Sachindranath Jayaraman , Vatsalkumar N. Mer

Let A be an m × n matrix with real entries. Given two proper cones K 1 and K 2 in ℝ n and ℝ m , respectively, we say that A is nonnegative if A ( K 1) ⊆ K 2. A is said to be semipositive if there exists a \(x \in K_1^ \circ \) such that \(Ax \in K_2^ \circ \). We prove that A is nonnegative if and only if A + B is semipositive for every semipositive matrix B . Applications of the above result are also brought out.

中文翻译:

相对于正确锥的非负性的刻画

A 为具有实数项的 m × n 矩阵。给定两个适当的锥 ķ 1 ķ 2在ℝ Ñ 和ℝ,分别,我们说 一个 非负如果 ķ 1)⊆ ķ 2。 如果存在一个\(x在K_1 ^ \ circ \中)使得\(Ax在K_2 ^ \ circ \中),则 A 被认为是半正的。我们证明,当且仅当对于每个半正矩阵 B, A + B 为半正值时 , A 是非负的 。还提出了上述结果的应用。
更新日期:2020-10-06
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