A note on Ostrowski%26apos;s Theorem

作者：Hadjidimos Apostolos^*

来源：Linear Algebra and Its Applications, 2013, 439(12): 3785-3795.

DOI：10.1016/j.laa.2013.10.009

• Ostrowski%26apos
• s Theorem
• Complex square irreducible matrices
• Weighted directed graphs

In this note, a further extension of Ostrowski%26apos;s Theorem, concerning mainly complex square irreducible matrices, is presented. Specifically, classes of irreducible matrices are determined for which the classical statement: %26quot;If for a matrix A = [a(ij)] is an element of C-nxn, n %26gt;= 2, relations vertical bar a(ij)vertical bar %26gt; (Sigma(n)(j=1)(,j not equal 1) vertical bar a(ij)vertical bar)(alpha) (Sigma(n)(j=1)(,j not equal 1) vertical bar a(ij)vertical bar)(1-alpha) are satisfied for all i is an element of {1, 2, ... , n} and for some alpha is an element of [0, 1], then, A is non-singular%26quot;, can hold even if all the inequalities in it turn out to be equalities.

• 出版日期2013-12-15