The LU-factorization of totally positive matrices
The LU-factorization of totally positive matrices
复制标题
全正矩阵的 LU 分解
DOI：
10.1016/0024-3795(73)90039-6
复制
发表时间：
1973
影响因子：
1.1
通讯作者：
C. Cryer
中科院分区：
文献类型：
--
作者：
C. Cryer
Ann×nreal matrix如果它的所有子矩阵都是严格正的，则表示一个stp（严格全正）矩阵。Ann×nreal三角矩阵是aΔSTPmatrix如果它所有的非平凡子阵都是严格正的。证明了他的反矩阵iffA= luwhereli是下三角矩阵，u是上三角矩阵，bothLandUareΔSTPmatrices。证明了几个相关结果。这些结果导致了stpmatrices的许多行列式性质的简单证明。
Ann×nreal matrixAis anSTP(strictly totally positive) matrix if all its minors are strictly positive. Ann×nreal triangular matrixAis aΔSTPmatrix if all its nontrivial minors are strictly positive. It is proved thatAis anSTPmatrix iffA=LUwhereLis a lower triangular matrix,Uis an upper triangular matrix, and bothLandUareΔSTPmatrices. Several related results are proved. These results lead to simple proofs of many of the determinantal properties ofSTPmatrices.