Exterior numerical radii and antiinvariant subspaces
學年 86
學期 2
出版（發表）日期 1998-07-01
作品名稱 Exterior numerical radii and antiinvariant subspaces
作品名稱（其他語言）
著者 譚必信; Tam, Bit-shun
單位 淡江大學數學學系
出版者 Taylor & Francis
著錄名稱、卷期、頁數 Linear and Multilinear Algebra 44(3), pp.195-245
摘要 Let m be a positive integer less than n, and let A B be n×n complex matrices. The mth A-exterior numerical radius of B is defined as where Cm( A) is the mth compound matrix of A and Un is the group of n×n unitary matrices. Marcus and Sandy conjectured that a (necessary and) sufficient condition for to imply that the rank of B is less than m is that A is nonscalar and counter-example to the conjecture was given in [10]. In this paper, using geometric arguments, we show that the conjecture is true in the special case when A is of rank m. Then we prove that in order that for each B of rank m it is necessary and sufficient that rank A≤m and rank (A—λI)≤min{m, n—m) for all complex numbers λ. We also find other equivalent conditions one of which is that, for any pair of linear subspaces X 9 Y of Cn with dim X= m and dim Y =n— m, there exists UεUn such that Cn = AU(X)⊗U(Y). To establish the equivalence of the above conditions, we give a structure theory of the anti-invariance of matrices, which relies on a combinatorial method and the use of gap between subspaces. As by-products, we obtain two interesting results about matchings of a multi-set. The cases when Unis replaced by GL(n, C) or the underlying field is the set of real numbers are also examined carefully. Some open problems are posed at the end.
關鍵字 mth A-exterior numerical radius;Marcus and Sandy conjecture;matching of a multi-set;antiinvariant subspace;gap between subspaces
語言 en
ISSN 0308-1087
期刊性質 國內
收錄於
產學合作
通訊作者
審稿制度 否
國別 TWN
公開徵稿
出版型式 ,電子版
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