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Stieltjes matrix : ウィキペディア英語版
Stieltjes matrix
In mathematics, particularly matrix theory, a Stieltjes matrix, named after Thomas Joannes Stieltjes, is a real symmetric positive definite matrix with nonpositive off-diagonal entries. A Stieltjes matrix is necessarily an M-matrix. Every ''n×n'' Stieltjes matrix is invertible to a nonsingular symmetric nonnegative matrix, though the converse of this statement is not true in general for ''n'' > 2.
From the above definition, a Stieltjes matrix is a symmetric invertible Z-matrix whose eigenvalues have positive real parts. As it is a Z-matrix, its off-diagonal entries are less than or equal to zero.
== See also ==

* Hurwitz matrix
* Metzler matrix

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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