P- and PN-matrices, Minkowski- and Metzler- matrices, and generalizations of the Stolper- Samuelson and Samuelson-Rybczynski theorems
P- and PN-matrices, Minkowski- and Metzler- matrices, and generalizations of the Stolper- Samuelson and Samuelson-Rybczynski theorems
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P 和 PN 矩阵、Minkowski 和 Metzler 矩阵以及 Stolper-Samuelson 和 Samuelson-Rybczynski 定理的推广
DOI：
10.1016/0022-1996(73)90006-8
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发表时间：
1973
影响因子：
3.3
通讯作者：
L. L. Wegge
中科院分区：
文献类型：
--
作者：
Yasuo Uekawa;M. Kemp;L. L. Wegge
我们论文的标题足够长，可以作为导言。我们只需要补充一点，这篇论文所涉及的问题与最近由奇普曼（1969），肯普和韦格（1969），肯普（1969，第1章），韦格和肯普（1969），库恩（1968），上川（1971）和稻田（1971）所研究的问题相似。集中在矩阵是非负的，我们建立了一个平行的那些也是P-矩阵和那些也是PN-矩阵，和矩阵之间的进一步平行，具有Minkowski属性的逆具有非负对角元素和非正非对角元素和那些具有Metzler属性的逆具有非正对角元素和非负非对角元素。然后，我们建立了Stolper-Samuelson和Samuelson-Rybczynski定理的几个推广。这些概括中的一些涉及到对生产投入（中间产品）的认识;所有这些都是产品和主要因素的总和，它们在数量上是任意的（但相等）。纯数学推导收集在第2节。经济问题留待第3节讨论。
The title of our paper is long enough to serve as its introduction. We need add only that the paper is concerned with problems similar rto those recently examined by Chipman (1969), Kemp and Wegge (1969), Kemp (1969, Appenchx to ch. l), Wegge and Kemp (1969), Kuhn (1968), Uekawa (1971) and Inada (1971). Concentrating on matrices which are non-negative, we establish a parallel between those which are also P-matrices and those which are also PN-matrices, and a further parallel between matrices which have the Minkowski property of possessing inverses with non-negative diagonal elements and non-positive off-diagonal elements and those which have the Metzler property of possessing inverses with non-positive diagonal elements and nonnegative off-diagonal elements. We then establish several generalizations of the Stolper-Samuelson and Samuelson-Rybczynski Theorems. Some of these generalizations involve the recognition of produced inputs (intermediate goods); all of them are in ternIs of products and primary factors which are arbitrary (but equal) in number. The purely mathematical derivations are collected in sect. 2. The economics is left to sect. 3.