论文标题
对称的三角形和五角核矩阵的完全阳性
The Complete Positivity of Symmetric Tridiagonal and Pentadiagonal Matrices
论文作者
论文摘要
我们提供了一个分解，足以显示何时何时具有对称的Tridiagonal矩阵$ A $是完全积极的。我们的分解可以应用于各种矩阵。我们为文献中的许多相关结果提供了替代证明，以简单明了的方式找到。我们表明，任何不可约合的三角形偶发矩阵的CP级别等于其等级。然后，我们考虑对称的五角大针矩阵，证明了一些类似的结果，并提供了两个不同的分解，足以完全阳性。我们用许多示例来说明我们的构造。
We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix $A$ is completely positive. Our decomposition can be applied to a wide range of matrices. We give alternate proofs for a number of related results found in the literature in a simple, straightforward manner. We show that the cp-rank of any irreducible tridiagonal doubly stochastic matrix is equal to its rank. We then consider symmetric pentadiagonal matrices, proving some analogous results, and providing two different decompositions sufficient for complete positivity. We illustrate our constructions with a number of examples.
