ON A THEOREM OF WIELANDT AND THE COMPOUNDS OF UNITARY MATRICES

被引:2
作者
DRURY, SW
机构
基金
加拿大自然科学与工程研究理事会;
关键词
D O I
10.1016/0024-3795(94)90362-X
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let A and B be normal endomorphisms with prescribed eigenvalues defined on a finite dimensional unitary space. A celebrated theorem of Wielandt states that the eigenvalues of A - B are forced to lie in a certain subset of the complex plane. The primary objective of this article is to extend Wielandt's result to give information about the joint distribution of the eigenvalues of A - B. The main tool in establishing this extension is a result on the compounds of unitary matrices. If U is an n X n unitary matrix, then Birkhoff's famous result on doubly stochastic matrices is often applied to write the matrix (\u(jk)\2)jk as a convex combination of permutation matrices. The natural generalization of this process to the compound of a unitary matrix is known to fail. Here we show that it succeeds if one considers only a certain restricted subset of entries.
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页码:391 / 412
页数:22
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